There are three guna-avataras, or incarnations of the qualitative modes of nature, and these are Brahma, Visnu and Siva

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Srimad-Bhagavatam

SB Canto 4

Brahmā, Viṣṇu and Maheśvara are called guṇa-avatāras, or incarnations of material qualities.
SB 4.6.43, Purport:

There are many types of energies of the Supreme Lord, and all of them are auspicious. Brahmā, Viṣṇu and Maheśvara are called guṇa-avatāras, or incarnations of material qualities. In the material world we compare these different incarnations from different angles of vision, but since all of them are expansions of the supreme auspicious, all of them are auspicious, although sometimes we consider one quality of nature to be higher or lower than another. The mode of ignorance, or tamo-guṇa, is considered very much lower than the others, but in the higher sense it is also auspicious. The example may be given herein that the government has both an educational department and criminal department. An outsider may consider the criminal department inauspicious, but from the government's point of view it is as important as the education department, and therefore the government finances both departments equally, without discrimination.

Lord Brahmā and Lord Śiva are qualitative incarnations of Viṣṇu, as guṇa-avatāras, and Viṣṇu with them accepts control of the quality of goodness; therefore He is also a qualitative incarnation like Lord Śiva and Lord Brahmā.
SB 4.7.51, Purport:

As explained in Bhagavad-gītā (7.5), jīva-bhūtāṁ mahā-bāho: the whole world is energy released from the supreme source, the Personality of Godhead, who, it is further stated in Bhagavad-gītā, acts in superior energies and inferior energies. The superior energy is the living entity, who is part and parcel of the Supreme Lord. As parts and parcels, the living entities are not different from the Supreme Lord; the energy emanated from Him is not different from Him. But in the actual activity of this material world, the living entity is under the different qualities of material energy and in different forms. There are 8,400,000 life forms. The same living entity acts under the influence of the different qualities of material nature. The entities have different bodies, but originally, in the beginning of creation, Lord Viṣṇu is alone. For the purpose of creation, Brahmā is manifested, and for annihilation there is Lord Śiva. As far as the spiritual entrance into the material world is concerned, all beings are part and parcel of the Supreme Lord, but under the covering of different material qualities they have different names. Lord Brahmā and Lord Śiva are qualitative incarnations of Viṣṇu, as guṇa-avatāras, and Viṣṇu with them accepts control of the quality of goodness; therefore He is also a qualitative incarnation like Lord Śiva and Lord Brahmā. Actually the different names exist for different directions, otherwise the origin is one only.

As far as this material world is concerned, Lord Brahmā, Lord Viṣṇu and Lord Śiva are all emanations from Kṛṣṇa. These three incarnations of Kṛṣṇa are called guṇa-avatāras.
SB 4.17.6-7, Purport:

Lord Kṛṣṇa is also known as avatārī, which means, "one from whom all the incarnations emanate." In Bhagavad-gītā (10.8) Lord Kṛṣṇa says, ahaṁ sarvasya prabhavo mattaḥ sarvaṁ pravartate: "I am the source of all spiritual and material worlds. Everything emanates from Me." Thus Lord Kṛṣṇa is the origin of everyone's appearance. As far as this material world is concerned, Lord Brahmā, Lord Viṣṇu and Lord Śiva are all emanations from Kṛṣṇa. These three incarnations of Kṛṣṇa are called guṇa-avatāras. The material world is governed by three material modes of nature, and Lord Viṣṇu, Lord Brahmā and Lord Śiva respectively take charge of the modes of goodness, passion and ignorance. Mahārāja Pṛthu is also an incarnation of those qualities of Lord Kṛṣṇa by which one rules over conditioned souls.

The three predominating deities of the material universe (Brahmā, Viṣṇu and Śiva) are called guṇa-avatāras.
SB 4.30.24, Purport:

In the previous verse it has been said (gṛhīta-māyā-guṇa-vigrahāya) that the Lord accepts three kinds of bodies (Viṣṇu, Brahmā and Śiva) for the purposes of creating, maintaining and annihilating the cosmic manifestation. The three predominating deities of the material universe (Brahmā, Viṣṇu and Śiva) are called guṇa-avatāras. There are many kinds of incarnations of the Supreme Personality of Godhead, and the first incarnations within this material world are Brahmā, Viṣṇu and Maheśvara (Śiva). Out of these three, Lord Brahmā and Lord Śiva accept material bodies, but Lord Viṣṇu does not accept a material body. Lord Viṣṇu is therefore known as viśuddha-sattva. His existence is completely free from the contamination of the material modes of nature. One should therefore not think that Lord Viṣṇu is in the same category with Lord Brahmā and Śiva. The śāstras forbid us to think in this way.

SB Canto 8

SB 8.5.21, Translation:

Lord Brahmā said: I, Lord Śiva, all of you demigods, the demons, the living entities born of perspiration, the living beings born of eggs, the trees and plants sprouting from the earth, and the living entities born from embryos—all come from the Supreme Lord, from His incarnation of rajo-guṇa (Lord Brahmā, the guṇa-avatāra) and from the great sages (ṛṣis) who are part of me. Let us therefore go to the Supreme Lord and take shelter of His lotus feet.

This prayer is actually offered to Lord Viṣṇu, the puruṣa, who in His incarnations as the guṇa-avatāras assumes the names Brahmā, Viṣṇu and Maheśvara.
SB 8.7.23, Translation and Purport:

O lord, you are self-effulgent and supreme. You create this material world by your personal energy, and you assume the names Brahmā, Viṣṇu and Maheśvara when you act in creation, maintenance and annihilation.

This prayer is actually offered to Lord Viṣṇu, the puruṣa, who in His incarnations as the guṇa-avatāras assumes the names Brahmā, Viṣṇu and Maheśvara.

The Supreme Personality of Godhead, Viṣṇu, resides within the material world as the sattva-guṇa-avatāra. Lord Śiva is the tamo-guṇa-avatāra, and Lord Brahmā is the rajo-guṇa-avatāra, but although Lord Viṣṇu is among them, He is not in the same category. Lord Viṣṇu is deva-deva, the chief of all the demigods.
SB 8.12.4, Purport:

The Supreme Personality of Godhead, Viṣṇu, resides within the material world as the sattva-guṇa-avatāra. Lord Śiva is the tamo-guṇa-avatāra, and Lord Brahmā is the rajo-guṇa-avatāra, but although Lord Viṣṇu is among them, He is not in the same category. Lord Viṣṇu is deva-deva, the chief of all the demigods. Since Lord Śiva is in this material world, the energy of the Supreme Lord, Viṣṇu, includes Lord Śiva. Lord Viṣṇu is therefore called jagad-vyāpī, "the all-pervading Lord." Lord Śiva is sometimes called Maheśvara, and so people think that Lord Śiva is everything. But here Lord Śiva addresses Lord Viṣṇu as Jagad-īśa, "the master of the universe." Lord Śiva is sometimes called Viśveśvara, but here he addresses Lord Viṣṇu as Jagan-maya, indicating that even Viśveśvara is under Lord Viṣṇu's control. Lord Viṣṇu is the master of the spiritual world, yet He controls the material world also, as stated in Bhagavad-gītā (mayādhyakṣeṇa prakṛtiḥ sūyate sacarācaram (BG 9.10)). Lord Brahmā and Lord Śiva are also sometimes called īśvara, but the supreme īśvara is Lord Viṣṇu, Lord Kṛṣṇa.

SB Canto 10.1 to 10.13

For the creation, maintenance and annihilation of this material world, the Lord appears as the guṇa-avatāras-Brahmā, Viṣṇu and Maheśvara.
SB 10.3 Summary:

Mother Devakī, being fully transcendental, sac-cid-ānanda, does not belong to this material world. Thus the Supreme Personality of Godhead appeared with four hands, as if born from her womb. Upon seeing the Lord in that Viṣṇu form, Vasudeva was struck with wonder, and in transcendental happiness he and Devakī mentally gave ten thousand cows in charity to the brāhmaṇas. Vasudeva then offered prayers to the Lord, addressing Him as the Supreme Person, Parabrahman, the Supersoul, who is beyond duality and who is internally and externally all-pervading. The Lord, the cause of all causes, is beyond material existence, although He is the creator of this material world. When He enters this world as Paramātmā, He is all-pervading (aṇḍāntara-stha-paramāṇu-cayāntara-stham (Bs. 5.35)), yet He is transcendentally situated. For the creation, maintenance and annihilation of this material world, the Lord appears as the guṇa-avatāras-Brahmā, Viṣṇu and Maheśvara. Thus Vasudeva offered prayers full of meaning to the Supreme Personality of Godhead.

Because Lord Brahmā and Lord Śiva are guṇa-avatāras and have exalted positions, they have some small sense of being like Kṛṣṇa.
SB 10.9.21, Purport:

Although the nitya-siddha expansions of Kṛṣṇa always remain with Kṛṣṇa, if those engaged in sādhana-siddhi follow in the footsteps of Kṛṣṇa's nitya-siddha associates, such sādhana-siddhas also can easily attain Kṛṣṇa without difficulty. But there are those who are attached to bodily concepts of life. Lord Brahmā and Lord Śiva, for example, have very prestigious positions, and thus they have the sense of being very exalted īśvaras. In other words, because Lord Brahmā and Lord Śiva are guṇa-avatāras and have exalted positions, they have some small sense of being like Kṛṣṇa. But the pure devotees who inhabit Vṛndāvana do not possess any bodily conception. They are fully dedicated to the service of the Lord in sublime affection, premā.

Sri Caitanya-caritamrta

CC Madhya-lila

The guṇa-avatāras are three—Lord Brahmā, Lord Śiva and Lord Viṣṇu.
CC Madhya 20.246, Translation and Purport:

"There are incarnations that control the material qualities (guṇa-avatāras), incarnations associated with the reign of each Manu (manvantara-avatāras), incarnations in different millenniums (yuga-avatāras) and incarnations of empowered living entities (śaktyāveśa-avatāras)."

The guṇa-avatāras are three—Lord Brahmā, Lord Śiva and Lord Viṣṇu (SB 10.88.3). The avatāras associated with the reign of each Manu, known as manvantara-avatāras, are listed as follows in Śrīmad-Bhāgavatam (Eighth Canto, chapters 1, 5 and 13): (1) Yajña, (2) Vibhu, (3) Satyasena, (4) Hari, (5) Vaikuṇṭha, (6) Ajita, (7) Vāmana, (8) Sārvabhauma, (9) Ṛṣabha, (10) Viṣvaksena, (11) Dharmasetu, (12) Sudhāmā, (13) Yogeśvara and (14) Bṛhadbhānu. All together these are fourteen in number, and of these, Yajña and Vāmana are also counted among the līlā-avatāras. All these manvantara incarnations are sometimes called vaibhava-avatāras.

Viṣṇu cannot be transformed into any form of material energy. Whenever there is association with māyā, the personality involved must be different from Lord Viṣṇu. Therefore Lord Śiva and Lord Brahmā are called guṇa-avatāras, for they associate with the material qualities.
CC Madhya 20.309, Purport:

Of the three deities supervising the creation, maintenance and dissolution of the universe, Lord Viṣṇu is never separate from the original Viṣṇu. However, Lord Śiva and Brahmā, due to their association with māyā, are different from Viṣṇu. Viṣṇu cannot be transformed into any form of material energy. Whenever there is association with māyā, the personality involved must be different from Lord Viṣṇu. Therefore Lord Śiva and Lord Brahmā are called guṇa-avatāras, for they associate with the material qualities. The conclusion is that Rudra is not exactly Lord Viṣṇu but rather a transformation of Viṣṇu. Therefore, he does not come within the category of the viṣṇu-tattvas. Thus he is inconceivably one with Viṣṇu and different from Him. The example given in this verse is very clear. Milk is compared to Viṣṇu. As soon as milk touches a sour substance, it becomes yogurt, or Lord Śiva. Although yogurt is constitutionally milk, it cannot be used in place of milk.

Other Books by Srila Prabhupada

Teachings of Lord Caitanya

There are three guṇa-avatāras, or incarnations of the qualitative modes of nature, and these are Brahmā, Viṣṇu and Śiva.
Teachings of Lord Caitanya, Chapter 7:

In Śrīmad-Bhāgavatam (10.46.31) it is said that Balarāma and Kṛṣṇa are the origin of all living entities and that these two personalities enter into everything. A list of incarnations is given in Śrīmad-Bhāgavatam (1.3), and they are as follows: (1) Kumāras, (2) Nārada, (3) Varāha, (4) Matsya, (5) Yajña, (6) Nara-nārāyaṇa, (7) Kārdami Kapila, (8) Dattātreya, (9) Hayaśīrṣa, (10) Haṁsa, (1 1) Dhruvapriya or Pṛśnigarbha, (12) Ṛṣabha, (13) Pṛthu, (14) Nṛsiṁha, (15) Kūrma, (16) Dhanvantari, (17) Mohinī, (18) Vāmana, (19) Bhārgava (Paraśurāma), (20) Rāghavendra, (21) Vyāsa, (22) Pralambāri Balarāma, (23) Kṛṣṇa, (24) Buddha (25) Kalki. Because almost all of these twenty-five līlā-avatāras appear in one day of Brahmā, which is called a kalpa, they are sometimes called kalpa-avatāras. Out of these, the incarnation of Haṁsa and Mohinī are not permanent, but Kapila, Dattātreya, Ṛṣabha, Dhanvantari and Vyāsa are five eternal forms, and they are more celebrated. The incarnations of the tortoise Kūrma, the fish Matsya, Nara-nārāyaṇa, Varāha, Hayaśīrṣa, Pṛśnigarbha, and Balarāma are considered to be incarnations of vaibhava. Similarly, there are three guṇa-avatāras, or incarnations of the qualitative modes of nature, and these are Brahmā, Viṣṇu and Śiva.

As far as the guṇa-avatāras, or qualitative incarnations of Viṣṇu, are concerned, they are three—Brahmā, Viṣṇu and Śiva.
Teachings of Lord Caitanya, Chapter 8:

As far as the guṇa-avatāras, or qualitative incarnations of Viṣṇu, are concerned, they are three—Brahmā, Viṣṇu and Śiva. Brahmā is one of the living entities, but due to his devotional service he is very powerful. This primal living entity, master of the mode of material passion, is directly empowered by the Garbhodakaśāyī Viṣṇu to create innumerable living entities. In Brahma-saṁhitā (5.49) Brahmā is likened to valuable jewels influenced by the rays of the sun, and the sun is likened to the Supreme Lord Garbhodakaśāyī Viṣṇu. If in some kalpa there is no suitable living entity capable of acting in Brahmā's capacity, Garbhodakaśāyī Viṣṇu Himself manifests as Brahmā and acts accordingly.

Lectures

Bhagavad-gita As It Is Lectures

Kṛṣṇa is the origin of Brahmā, Viṣṇu, Maheśvara. They are guṇa-avatāra.
Lecture on BG 7.7 -- Vrndavana, August 13, 1974:

In another place Kṛṣṇa says, aham ādir hi devānām (Bg 10.2). He is the origin of all demigods. The principal demigods are Viṣṇu and Maheśvara and... Maheśvara means Lord Śiva. And Brahmā. Brahmā, Viṣṇu, Maheśvara. So Kṛṣṇa is the origin of Brahmā, Viṣṇu, Maheśvara. They are guṇa-avatāra. For maintaining this material world... The material world is composed of three guṇas: sattva, rajas, tamas. So the director of the sattva-guṇa department is Lord Viṣṇu, and the director of the rajo-guṇa department is Lord Brahmā, and the director of the tamo-guṇa department is Lord Śiva. Origin is Kṛṣṇa. Therefore in the Śrīmad-Bhāgavatam it is concluded after describing all the incarnations of God, different incarnations, the conclusion is made, ete cāṁśa-kalāḥ puṁsaḥ kṛṣṇas tu bhagavān svayam: (SB 1.3.28) "All the incarnations mentioned in this chapter, they are either expansion of the Supreme Personality of Godhead or expansion of the expansion, secondary expansion."

Srimad-Bhagavatam Lectures

Viṣṇu also one of the devas, first, principle devas. Brahmā, Viṣṇu, Maheśvara. Brahmā, Lord Viṣṇu, and Lord Śiva. Guṇāvatāra. Viṣṇu expanding Himself in three avatāras.
Lecture on SB 1.7.51-52 -- Vrndavana, October 8, 1976:

Actually, sometimes it is said that Kṛṣṇa is the incarnation of Viṣṇu, but actually Viṣṇu is incarnation of Kṛṣṇa. Aham ādir hi devānām (Bg 10.2), that is said in the Bhagavad-gītā. Viṣṇu also one of the devas, first, principle devas. Brahmā, Viṣṇu, Maheśvara. Brahmā, Lord Viṣṇu, and Lord Śiva. Guṇāvatāra. Viṣṇu expanding Himself in three avatāras. Sattva-guṇa He takes charge Himself, sattva-guṇa. Rajo-guṇa it is given to Brahmā in charge, and tamo-guṇa is given to the Lord Śiva. Sṛṣṭi-sthiti-pralaya. Sṛṣṭi, creation, is done by Brahmā, rajo-guṇa; and sthiti, maintenance, is done by Viṣṇu; and destruction is done by Lord Śiva, tamo-guṇa. He is not tamo-guṇa. In charge of tamo-guṇa. Just like somebody becomes superintendent of jail. It does not mean that the superintendent is also one of the prisoners. No. He's in charge of the jail department. Similarly, Lord Śiva, He's not in tamo-guṇa. He's transcendental. He is almost Viṣṇu. He's neither ordinary human being. Lord Śiva is in between viṣṇu-tattva and jīva-tattva. So how he can be in the tamo-guṇa? Nobody is... They are all transcendental. Especially Lord Viṣṇu.

These three departments are there. So for creative department of this material world, Lord Brahma; for maintenance department, Lord Viṣṇu Himself; and for destruction, Lord Śiva. These are the guṇa avatāras, three, trinity.
Lecture on SB 7.9.11-13 -- Hawaii, March 24, 1969:

So these qualities will work because this material world—one side, goodness; another side, darkness; another side, activity. This is going on. So as there are so many departments of activities, all these demigods, they are in charge of, director, director in chief. So brahmādayaḥ. Brahmā is in charge of something. Indra is in charge of something. The demigods, they're officers. They have no information. They say, "It is nature, nature, nature, nature." No nature. They are department, department. Indra is in charge of this cloud, how cloud is conducted, how rain falls there, and he's in charge of... Water department, like that. Just like moon. Moon is in charge of lighting at night. Sun is in charge of lighting in daytime. Because it is darkness. The whole world is darkness. So these demigods... Similarly, Lord Śiva is in charge of destroying, tamo-guṇa. When there will be necessity of destroying this whole thing... Because this world is like that. Everything that is created, that must be destroyed. Your body is being created from the father and mother. Now it is being maintained. So creation and maintenance, and then a time will come—it will be destroyed. So these, these three departments are there. So for creative department of this material world, Lord Brahma; for maintenance department, Lord Viṣṇu Himself; and for destruction, Lord Śiva. These are the guṇa avatāras, three, trinity. One is creating, one is maintaining...

Creation, maintenance and destruction, three things are going on on account of presence of the Supreme Soul. Therefore the three principal deities—Brahmā, Viṣṇu, Maheśvara—are there, guṇa-avatāra. He is not within the guṇa; therefore He expands Himself as guṇāvatāra: sattva-guṇa, rajo-guṇa, tamo-guṇa. But He's turya of the guṇas.
Lecture on SB 7.9.32 -- Mayapur, March 10, 1976:

So the same principle is applicable to the whole cosmic creation, that even within the ant the same principle, within Brahmā the same principle, and within the gigantic universe, the same principle. Without the spirit soul, there is no question of creation. Creation, maintenance and destruction, three things are going on on account of presence of the Supreme Soul. Therefore the three principal deities—Brahmā, Viṣṇu, Maheśvara—are there, guṇa-avatāra. He is not within the guṇa; therefore He expands Himself as guṇāvatāra: sattva-guṇa, rajo-guṇa, tamo-guṇa. But He's turya of the guṇas. Just like if we enter into the fire, we'll be burned, but sometimes the fire brigade men, they enter into the fire... They have got suit and contradictory dress that they can enter into the fire. Similarly, māyā... Māyā is very strong, but Kṛṣṇa, the Lord, when He comes within this material world—yuge yuge sambhavāmy ātma-māyayā (BG 4.6)—He comes in His own original turya status. He does not become affected. Guṇāṁś ca yuṅkṣe. He's not affected. This is the position of Kṛṣṇa. He's always transcendental.

Sri Caitanya-caritamrta Lectures

Viṣṇu creates, and Lord Śiva annihilates, and Brahmā is in charge of this universe.
Lecture on CC Madhya-lila 20.281-293 -- New York, December 18, 1966:

"Now, this Viṣṇu has nothing to do. He is not affected by this material contamination." That is the power of Viṣṇu. Just we are living entities. When we come into this material world, we become contaminated, we become affected by the influence of this material nature. But Viṣṇu, although He is looking after the management of creation of this brahmāṇḍa, He is not affected. He is not affected.

'viṣṇu'-rūpa hañā kare jagat pālane
guṇātīta viṣṇu-sparśa nāhi māyā-sane
'rudra'-rūpa dhari kare jagat saṁhāra

And when these material worlds or universes are to be annihilated, the same Viṣṇu in His form of Lord Śiva, Rudra-rūpa, He annihilates. So Viṣṇu creates, and Lord Śiva annihilates, and Brahmā is in charge of this universe.

brahmā, viṣṇu, śiva-tāṅra guṇa-avatāra
sṛṣṭi-sthiti-pralayera tinera adhikāra

Now, this material world is created, it is, it stays for some time, and it is again annihilated. Just we have seen in the Bhagavad-gītā, bhūtvā bhūtvā pralīyate (BG 8.19). This is the nature. This material nature is like that. Just like you have seen one lamp. Once it is extinguished; once it is light. Similarly, there is creation, there is maintenance and there is annihilation of this material world. Now, these three functions are controlled by three guṇāvatāras, qualitative incarnation of the Supreme Lord.

Just like to a carpenter you give wood and planks and materials and screw and other thing, and the carpenter makes a very good cabinet, and you maintain that, similarly, this brahmāṇḍa, the secondary creation, is Brahmā, and Viṣṇu is the maintainer, and when it is to be destroyed, it is destroyed by Lord Śiva. These three guṇāvatāras. Brahmā, viṣṇu, siva-tāṅra guṇa-avatāra.
Lecture on CC Madhya-lila 20.281-293 -- New York, December 18, 1966:

Viṣṇu is the incarnation of the modes of goodness, and Śiva is the incarnation of the modes of annihilation, and Brahmā is the in-charge. Brahmā is secondary. Brahmā is the secondary creator. First of all, the everything is, the principle, the material principle ingredients and the guṇas and the everything is created by Viṣṇu. Then, the secondary creation, with those ingredients, all these planetary system, everything, is created by Brahmā. So Brahmā is also a secondary creator. And then Viṣṇu maintains. Just like to a carpenter you give wood and planks and materials and screw and other thing, and the carpenter makes a very good cabinet, and you maintain that, similarly, this brahmāṇḍa, the secondary creation, is Brahmā, and Viṣṇu is the maintainer, and when it is to be destroyed, it is destroyed by Lord Śiva. These three guṇāvatāras. Brahmā, viṣṇu, siva-tāṅra guṇa-avatāra. They are incarnations of Kṛṣṇa's guṇa. So in other words, it is to be understood that these three guṇas, they are also coming from Kṛṣṇa, three guṇas. So therefore, for Kṛṣṇa, there is no such distinction.

In the Vedas there is a prayer, Sahasra-śīrṣā. That is very famous prayer. That prayer is offered to this Viṣṇu. Which Viṣṇu? The Garbhodakaśāyī Viṣṇu, the Viṣṇu who has entered in every universe.
Lecture on CC Madhya-lila 20.281-293 -- New York, December 18, 1966:

Similarly, these distinctions, these qualitative distinctions, matter, spirit, and the different kinds of modes, they are distinction for us, not for Kṛṣṇa. He is Absolute. He is Absolute. To the Absolute, there is no such distinction. Therefore when Kṛṣṇa comes, when Kṛṣṇa comes in this material, He is not affected by this. Suppose the minister, the secretary of the president, goes to the criminal department to see the prison house. He is not affected by the prison rules. It is simple to understand. If the prisoner thinks, "Oh, he is also one of the prisoners because he has come here," this is nonsense. He is not prisoner. Similarly, when Kṛṣṇa comes in this material world, if a foolish man thinks that he is also one of us, he is foolish number one. Therefore in the Bhagavad-gītā it is stated, avajānanti māṁ mūḍhā mānuṣīṁ tanum āśritāḥ: (BG 9.11) "Foolish persons, they think that I am one of them." These examples are very nice. We can understand.

So here it is stated that Viṣṇu...,

brahmā, viṣṇu, śiva-tāṅra guṇa-avatāra
sṛṣṭi-sthiti-pralayera tinera adhikāra
hiraṇyagarbha-antaryāmi-garbhodakaśāyī
'sahasra-śīrṣādi' kari' vede yāṅre gāi

In the Vedas there is a prayer, Sahasra-śīrṣā. That is very famous prayer. That prayer is offered to this Viṣṇu. Which Viṣṇu? The Garbhodakaśāyī Viṣṇu, the Viṣṇu who has entered in every universe, that Garbhodakaśāyī Viṣṇu.

Now on these three qualities, material modes of nature, the heads are Brahmā-Brahmā, the first living creature, Brahmā—and Viṣṇu—Viṣṇu, God Himself.
Lecture on CC Madhya-lila 20.298 -- New York, December 20, 1966:

There are three qualities in the material world: goodness, passion and ignorance. So each quality is controlled by the Supreme Lord Himself by His expansion of different incarnation. Brahmā, viṣṇu, śiva—tina guṇa avatāra. Now on these three qualities, material modes of nature, the heads are Brahmā-Brahmā, the first living creature, Brahmā—and Viṣṇu—Viṣṇu, God Himself—and Śiva, Lord Śiva. Śiva's position is between Brahmā and Viṣṇu. Viṣṇu is God, and Brahmā is living entity. Gradation. Living entities, they are also parts and parcels of God. Śiva is also part and parcel of God. Viṣṇu is also part and parcel of God. But there are degrees of power. That we have already discussed. Kṛṣṇa is cent percent, Viṣṇu is ninety-four percent, Śiva is eighty-four percent, and we living entities, we are seventy-eight percent. So tri-guṇa aṅgīkari' kare sṛṣṭy-ādi-vyavahāra. They have nothing to do with these material modes of nature. Just like a person in charge of the criminal department or jail department, but we should not think that he is also one of the prisoners because he is in charge of the jail department.

General Lectures

Sarvam means the creative deities: Brahma, Viṣṇu, Maheśvara. They are also from Kṛṣṇa. The Brahma, Viṣṇu, Maheśvara are called guṇa-avatāras of Kṛṣṇa, incarnation of the material qualities.
Lecture -- Bombay, March 19, 1972:

Sarva-kāraṇa-kāraṇam. In the Bhagavad-gītā it is also said, ahaṁ sarvasya prabhavaḥ mattaḥ sarvaṁ pravartate (BG 10.8). Sarvam means the creative deities: Brahma, Viṣṇu, Maheśvara. They are also from Kṛṣṇa. The Brahma, Viṣṇu, Maheśvara are called guṇa-avatāras of Kṛṣṇa, incarnation of the material qualities. Brahma is incarnation of the material quality passion, rajo-guṇa, and Viṣṇu is incarnation of the quality sattva-guṇa, and Lord Siva is the incarnation of the Supreme Personality of Godhead in tama-guṇa. So the example is explained in Śrīmad-Bhāgavatam also, what is the difference between Lord Siva, Lord Brahma and Lord Viṣṇu. The difference is they are one but they are different manifestations. Just like firewood. In the wood there is fire. So in the beginning there is no fire, but when there is little fire, there is smoke, then there is ignition, flame. But we are concerned with the flame, neither with the wood nor with the smoke. Similarly, although Lord Siva, Lord Viṣṇu and Lord Brahma are different manifestations of the same thing, Absolute Truth, still we are concerned with the fire of Viṣṇu, not with the wood, nor with the smoke. This is the conclusion of Śrīmad-Bhāgavatam.

Philosophy Discussions

The material creation is done by personal expansion primarily—the whole material ingredients, and then with the ingredients the guṇa-avatāra, Brahmā, he creates particularly. And Lord Śiva, when the time is right, he annihilates.
Philosophy Discussion on Origen:

Prabhupāda: So our conception is—"our" means Vedic conception—that Kṛṣṇa is the original Personality of Godhead, as it is confirmed in the Bhagavad-gītā, ahaṁ sarvasya prabhavaḥ: (BG 10.8) "I am the origin of everyone." Either you call the son or the Holy Ghost, it doesn't matter, but the Supreme Personality of Godhead is the origin. Then, He has got expansion. That expansion is not actually His son... Or there are two kinds of expansion: His personal expansions and His expansion as part and parcel. His personal expansion is called Viṣṇu-tattva, and the part and parcel expansion is called jīva-tattva—in Sanskrit technical words, svāṁśa and vibhinnāṁśa. The personal expansion there are also many varieties—puruṣa-avatāra, saktyāveśa-avatāra, manvantara-avatāra, many varieties. So generally, His personal expansion for creation of this material world are three also, accepted as Brahmā, Viṣṇu, Maheśvara. Viṣṇu is personal expansion, and Brahmā is expansion of the living entity, or the vibhinnāṁśa. And another expansion, via-media between the personal expansion and expansion of jīva, the via-media expansion is called Śiva. So the material creation is done by personal expansion primarily—the whole material ingredients, and then with the ingredients the guṇa-avatāra, Brahmā, he creates particularly. And Lord Śiva, when the time is right, he annihilates. So this creation, material creation, is created, maintained for sometimes, and again dissolved or annihilated.