According to the Vaiṣṇava almanac, the twelve months of the year are named according to the twelve Vaikuṇṭha forms of Lord Kṛṣṇa, and these forms are known as the predominating Deities for the twelve months. This calendar begins with the month of Mārgaśīrsa, which is equivalent to late October and early November. The remainder of November is known by Vaiṣṇavas as Keśava. December is called Nārāyaṇa, January is called Mādhava, February is Govinda, March is Viṣṇu, April Śrī Madhusūdana, May Trivikrama, June Vāmana, July Śrīdhara, August Hṛṣīkeśa, September Padmanābha, and early October is known as Dāmodara. (The name Dāmodara was given to Kṛṣṇa when He was bound by ropes by His mother, but the Dāmodara form in the month of October is a different manifestation). Just as the months of the year are known according to the twelve different names of the Supreme Lord, the Vaiṣṇava community marks twelve parts of the body according to these names. For instance, the tilaka mark on the forehead is called Keśava, and on the stomach, breast and arms the other names are also given. These are the same names as those given the months.
The four forms (Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha) are also expanded in the vilāsa-mūrti. These are eight in number, and their names are Puruṣottama, Acyuta, Nṛsiṁha, Janārdana, Hari, Kṛṣṇa, Adhokṣaja and Upendra. Out of these eight, Adhokṣaja and Puruṣottama are the vilāsa forms of Vāsudeva. Similarly, Upendra and Acyuta are the forms of Saṅkarṣaṇa; Nṛsiṁha and Janārdana are the forms of Pradyumna, and Hari and Kṛṣṇa are the vilāsa forms of Aniruddha. (This Kṛṣṇa is different from the original Kṛṣṇa.)
These twenty-four forms are known as the vilāsa manifestation of the prābhava (four-handed) form, and they are named differently according to the position of the symbolic representations (mace, disc, lotus flower and conch shell). Out of these twenty-four forms there are vilāsa and vaibhava forms. Names mentioned herein, such as Pradyumna, Trivikrama, Vāmana, Hari and Kṛṣṇa, are also different in features. Then, coming to the prābhava-vilāsa of Kṛṣṇa (including Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha), there are a total of twenty further variations. All of these have Vaikuṇṭha planets in the spiritual sky and are situated in eight different directions. Although each of them is eternally in the spiritual sky, some of them are nonetheless manifest in the material world also.
In the spiritual sky all the planets dominated by the Nārāyaṇa feature are eternal. The topmost planet in the spiritual sky is called Kṛṣṇaloka and is divided into three different portions: Gokula, Mathurā and Dvārakā. In the Mathurā portion, the form of Keśava is always situated. He is also represented on this earthly planet. In Mathurā, India, the Keśava mūrti is worshiped, and similarly there is a Puruṣottama form in Jagannātha Purī in Orissa. In Ānandāraṇya there is the form of Viṣṇu, and in Māyāpur, the birthplace of Lord Caitanya, there is the form of Hari. Many other forms are also situated in various places on the earth. Not only in this universe but in all other universes as well the forms of Kṛṣṇa are distributed everywhere. It is indicated that this earth is divided into seven islands, which are the seven continents, and it is understood that on each and every island there are similar forms, but at the present moment these are found only in India. Although from Vedic literatures we can understand that there are forms in other parts of the world, at present there is no information of their location.
The different forms of Kṛṣṇa are distributed throughout the universe to give pleasure to the devotees. It is not that devotees are born only in India. There are devotees in all parts of the world, but they have simply forgotten their identity. These forms incarnate not only to give pleasure to the devotee but to reestablish devotional service and perform other activities which vitally concern the Supreme Personality of Godhead. Some of these forms are incarnations mentioned in the scriptures, such as the Viṣṇu incarnation, Trivikrama incarnation, Nṛsiṁha incarnation and Vāmana incarnation.
In the Siddhārtha-saṁhitā, there is a description of the twenty-four forms of Viṣṇu, and these forms are named according to the position of the symbolic representations in Their four hands. When one describes the positions of objects in the hands of the Viṣṇu mūrti, one should begin with the lower right hand then move to the upper right hand, upper left hand and, finally, to the lower left hand. In this way, Vāsudeva may be described as being represented by mace, conch shell, disc and lotus flower. Saṅkarṣaṇa is represented by mace, conch shell, lotus flower and disc. Similarly, Pradyumna is represented by disc, conch shell, mace and lotus flower. Aniruddha is represented by disc, mace, conch shell and lotus flower. In the spiritual sky the representations of Nārāyaṇa are twenty in number and are described as follows: Śrī Keśava (flower, conch shell, disc, mace), Nārāyaṇa (conch, flower, mace and disc), Śrī Mādhava (mace, disc, conch and flower), Śrī Govinda (disc, mace, flower and conch), Viṣṇu-mūrti (mace, flower, conch and disc), Madhusūdana (disc, conch, flower and mace), Trivikrama (flower, mace, disc and shell), Śrī Vāmana (conch, disc, mace and flower), Śrīdhara (flower, disc, mace and shell), Hṛṣīkeśa (mace, disc, flower and conch), Padmanābha (shell, flower, disc and mace), Dāmodara (flower, disc, mace and shell), Puruṣottama (disc, flower, shell and mace), Acyuta (mace, flower, disc and shell), Nṛsiṁha (disc, flower, mace and shell), Janārdana (flower, disc, shell and mace), Śrī Hari (shell, disc, flower and mace), Śrī Kṛṣṇa (shell, mace, flower and disc), Adhokṣaja (flower, mace, shell and disc), and Upendra (shell, mace, disc and flower).
According to the Hayaśīrṣa-pañcarātra, there are sixteen forms, and these forms are named differently according to the situations of the disc and mace. The conclusion is that the Supreme Original Personality of Godhead is Kṛṣṇa. He is called līlā-puruṣottama, and He resides principally in Vṛndāvana as the son of Nanda. It is also learned from the Hayaśīrṣa-pañcarātra that there are nine forms protecting each of the two Purīs known as the Mathurā Purī and the Dvārakā Purī: Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha protect one, and Nārāyaṇa, Nṛsiṁha, Hayagrīva, Varāha and Brahmā—protect the other. These are different manifestations of the prakāśa and vilāsa forms of Lord Kṛṣṇa.
Lord Caitanya also informs Sanātana Gosvāmī that there are different forms of svāṁśa as well, and these are divided into the Saṅkarṣaṇa division and the incarnation division. From the first division come the three puruṣa-avatāras—the Kāraṇodakaśāyī Viṣṇu, Garbhodakaśāyī Viṣṇu and Kṣīrodakaśāyī Viṣṇu—and from the other division come the līlā-avatāras, such as the Lord's incarnations as a fish, tortoise, etc.
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.
It is thus safe to conclude that there is no end to the expansions and incarnations of Kṛṣṇa. Lord Caitanya explains some of them to Sanātana just to give him an idea of how the Lord expands and enjoys. These conclusions are also confirmed in Śrīmad-Bhāgavatam (SB 1.3.26). There it is said that there is no limit to the incarnations of the Supreme Lord, just as there is no limit to the waves of the ocean.
Kṛṣṇa first incarnates as the three puruṣa-avatāras, namely the Mahā-Viṣṇu or Kāraṇodakaśāyī avatāra, the Garbhodakaśāyī avatāra and the Kṣīrodakaśāyī avatāra. This is confirmed in the Sātvata-tantra. Kṛṣṇa's energies can also be divided into three: His energy of thinking feeling and acting. When He exhibits His thinking energy, He is the Supreme Lord; when He exhibits His feeling energy, He is Lord Vāsudeva; when He exhibits His acting energy, He is Saṅkarṣaṇa Balarāma. Without His thinking, feeling and acting, there would be no possibility of creation. Although there is no creation in the spiritual world—for there the planets are beginningless—there is creation in the material world. In either case, however, both the spiritual and material worlds are manifestations of the energy of acting, in which Kṛṣṇa acts in the form of Saṅkarṣaṇa and Balarāma.
The spiritual world of the Vaikuṇṭha planets and Kṛṣṇaloka, the supreme planet, is situated in His energy of thinking. Although there is no creation in the spiritual world, which is eternal, it is still to be understood that the Vaikuṇṭha planets depend on the thinking energy of the Supreme Lord. This thinking energy is described in Brahma-saṁhitā (5.2), where it is said that the supreme abode, known as Goloka, is manifested like a lotus flower with hundreds of petals. Everything there is manifested by Ananta, the Balarāma or Saṅkarṣaṇa form. The material cosmic manifestation and its different universes are manifest through māyā, or material energy. However, one should not think that material nature or material energy is the cause of this cosmic manifestation. Rather, it is caused by the Supreme Lord, who uses His different expansions through material nature. In other words, there is no possibility of any creation without the superintendence of the Supreme Lord. The form by which the energy of material nature works to bring about creation is called the Saṅkarṣaṇa form, and it is understood that this cosmic manifestation is created under the superintendence of the Supreme Lord.
In Śrīmad-Bhāgavatam (SB 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.
Of the manvantara-avatāras, there are fourteen: (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, (14) Bṛhadbhānu. Out of these fourteen manvantara-avatāras, Yajña and Vāmana are also līlā-avatāras, and the rest are manvantara-avatāras. These fourteen manvantara-avatāras are also known as vaibhava-avatāras.The four yuga-avatāras are also described in Śrīmad-Bhāgavatam. In the Satya-yuga, the incarnation of God is white; in the Tretā-yuga He is red; in the Dvāpara-yuga, He is blackish; and in the Kali-yuga He is also blackish, but sometimes, in a special Kali-yuga, His color is yellowish (as in the case of Caitanya Mahāprabhu). As far as the śaktyāveśa-avatāras are concerned, they include Kapila and Ṛṣabha, Ananta, Brahmā (sometimes the Lord Himself becomes Brahmā), Catuḥsana (the incarnation of knowledge), Nārada (the incarnation of devotional service), King Pṛthu (the incarnation of administrative power), and Paraśurāma (the incarnation who subdues evil principles).