In this verse the word śiva-śakti is significant. Śiva means "auspicious," and śakti means "energy." 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.
(Srimad Bhagavatam----4:6:43----purport).

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.
(Srimad Bhagavatam----4:7:51----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.
(Srimad Bhagavatam----4:17:6-7----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.
(Srimad Bhagavatam----4:30:24----purport).

The Supreme Personality of Godhead has different varieties of incarnations, including the guṇa-avatāras, manvantara-avatāras, līlā-avatāras and yuga-avatāras, all of which are described in the śāstras. Without reference to the śāstras there can be no question of accepting anyone as an incarnation of the Supreme Personality of Godhead. Therefore, as especially mentioned here, gṛṇanti kavayaḥ: the descriptions of various incarnations are accepted by great learned scholars with perfect intelligence. At the present time, especially in India, so many rascals are claiming to be incarnations, and people are being misled. Therefore, the identity of an incarnation should be confirmed by the descriptions of the śāstras and by wonderful activities. As described in this verse by the word mahīyasaḥ, the activities of an incarnation are not ordinary magic or jugglery, but are wonderful activities.
(Srimad Bhagavatam----8:1:2----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 (B.G.9:10).
(Srimad Bhagavatam----8:12:4----purport).

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. Devakī followed her husband by offering prayers describing the transcendental nature of the Lord. Fearing Kaṁsa and desiring that the Lord not be understood by atheistic and materialistic nondevotees, she prayed that the Lord withdraw His transcendental four-armed form and appear like an ordinary child with two hands.
(Srimad Bhagavatam----10:3----summary).

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. Śrī Caitanya Mahāprabhu has therefore recommended, premā pum-artho mahān: the highest perfection of life is premā, pure love in relationship with Kṛṣṇa. And mother Yaśodā appears to be the topmost of devotees who have attained this perfection.
(Srimad Bhagavatam----10:9:21----purport).

First they discussed the constitutional position of the living entities, and Śrī Caitanya Mahāprabhu explained to Sanātana Gosvāmī how the living entity is one of Lord Kṛṣṇa's energies. After this, the Lord explained the way of devotional service. While discussing the Absolute Truth, Śrī Kṛṣṇa, the Lord analyzed Brahman, Paramātmā and Bhagavān, as well as the expansions of the Lord called svayaṁ-rūpa, tad-ekātma and āveśa, which are divided into various branches known as vaibhava and prābhava. Thus the Lord described the many forms of the Supreme Personality of Godhead. He also described the incarnations of God within the material world, incarnations such as the puruṣa-avatāras, manvantara-avatāras, guṇa-avatāras and śaktyāveśa-avatāras. The Lord also discussed the divisions of Kṛṣṇa's different ages, such as bālya and paugaṇḍa, and the different pastimes of the different ages. He explained how Kṛṣṇa attained His permanent form when He reached youth. In this way Śrī Caitanya Mahāprabhu explained and described everything to Sanātana Gosvāmī.
(Sri Caitanya Caritamrta-- 2:20:--summary).

The guṇa-avatāras are three—Lord Brahmā, Lord Śiva and Lord Viṣṇu (S.B.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.
(Sri Caitanya Caritamrta---- 2:20:246----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.
(Sri Caitanya Caritamrta---- 2:20:309----purport).

There are six kinds of incarnations: (1) the puruṣa-avatāra, (2) the līlā-avatāra, (3) the guṇa-avatāra, (4) the manvantara-avatāra, (5) the yuga-avatāra, and (6) the śaktyāveśa-avatāra. Out of the six vilāsa manifestations of Kṛṣṇa, there are two divisions based on His age, and these are called bālya and paugaṇḍa. As the son of Nanda Mahārāja, Kṛṣṇa in His original form enjoys both of these childhood aspects—namely bālya and paugaṇḍa.
(Teachings of Lord Caitanya).

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.
(Teachings of Lord Caitanya).

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.
(Teachings of Lord Caitanya).

After describing the Līlā and guṇa-avatāras, Lord Caitanya explains the manvantara-avatāras to Sanātana Gosvāmī. He first states that there is no possibility of counting the manvantara-avatāras. In one kalpa, or one day of Brahmā, fourteen Manus are manifest. One day of Brahmā is calculated at 4 billion 320 million years, and Brahmā lives for one hundred years on this scale. Thus if fourteen Manus appear in one day of Brahmā, there are 420 Manus during one month of Brahmā, and during one year of Brahmā there are 5,040 Manus. Since Brahmā lives for one hundred of his years, it is calculated that there are 504,000 Manus manifest during the lifetime of one Brahmā. Since there are innumerable universes, no one can imagine the totality of the manvantara incarnations.
(Teachings of Lord Caitanya).

The puruṣa-avatāras are the Lords of the universal creation. These are Kāraṇodakaśāyī Viṣṇu, Garbhodakaśāyī Viṣṇu and Kṣīrodakaśāyī Viṣṇu. There are also līlā-avatāras, and these include (1) Catuḥsana, or the four Kumāras, (2) Nārada, (3) Varāha, (4) Matsya, (5) Yajña, (6) Nara-Nārāyaṇa, (7) Kārdami Kapila, (8) Dattātreya, (9) Hayaśīrṣā, (10) Haṁsa, (11) 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 and (25) Kalki.
These twenty-five Personalities of Godhead are known as līlā-avatāras. Because they appear in each day of Brahmā, or in each kalpa (millennium), they are sometimes known as kalpa-avatāras. Of these incarnations, Haṁsa and Mohinī are neither permanent nor very well known, but They are listed among the prābhava-avatāras. Kapila, Dattātreya, Ṛṣabha, Dhanvantari and Vyāsa are eternally situated and very widely known. They are also counted among the prābhava incarnations. Kūrma, Matsya, Nārāyaṇa, Varāha, Hayagrīva, Pṛśnigarbha and Baladeva, the killer of Pralambāsura, are counted among the vaibhava-avatāras.
(Sri Caitanya Caritamrta---- 2:20:244----purport).