By devotional service one can understand that Kṛṣṇa first of all manifests Himself as svayaṁ-rūpa, His personal form, then as tad-ekātma-rūpa, and then as āveśa-rūpa. It is in these three features that He manifests Himself in His transcendental form. The feature of svayaṁ-rūpa is the form by which Kṛṣṇa can be understood by one who may not understand His other features. In other words, the form by which Kṛṣṇa is directly understood is called svayaṁ-rūpa, or His personal form. The tad-ekātma-rūpa is that form which most resembles the svayaṁ-rūpa, but there are some differences in the bodily features. The tad-ekātma-rūpa is divided into two manifestations: the personal expansion (svāṁśa) and the pastime expansion (vilāsa). As far as the āveśa-rūpa is concerned, when Kṛṣṇa empowers some suitable living entity to represent Him, that living entity is called āveśa-rūpa or śaktyāveśa-avatāra.

The personal form of Kṛṣṇa can be divided into two: svayaṁ-rūpa and svayaṁ-prakāśa. As far as His svayaṁ-rūpa (or pastime form) is concerned, it is in that form that He remains always in Vṛndāvana with the inhabitants of Vṛndāvana. This personal form (svayaṁ-rūpa) can be further divided into the prābhava and vaibhava forms. For example, Kṛṣṇa expanded Himself in multiple forms during the rāsa dance in order to dance with each and every gopī who took part in that dance. Similarly, He expanded Himself into 16,108 forms in Dvārakā when he married 16,108 wives. There are some instances of great mystics’ expanding their bodily forms by the yoga process, but Kṛṣṇa did not expand Himself in that way. In Vedic history, Saubhari Ṛṣi expanded himself into eight forms by the yoga process, but those expansions were simply reflections, for Saubhari remained one. But when Kṛṣṇa manifested Himself in different forms, each and every one of them was a separate individual. When Nārada Muni visited Kṛṣṇa at His different palaces in Dvārakā, he was astonished at this, and yet Nārada is never astonished to see the expansions of a yogī’s body, since he knows the trick himself.

Śrīmad-Bhāgavatam describes Nārada Muni’s astonishment at seeing Kṛṣṇa’s expansions in Dvārakā. Nārada wondered how the Lord was present with His queens in each and every one of His 16,108 palaces. With each queen, Kṛṣṇa Himself was in a different form, acting in different ways. In one form He was talking with His wife, in another form He was petting His children, and in another form He was performing some household duty. These different activities are conducted by the Lord when He is in His “emotional” forms, which are known as vaibhava-prakāśa expansions. Similarly, there are other unlimited expansions of Kṛṣṇa’s forms, but even when they are divided or expanded without limit, they are still one and the same. There is no difference between one form and another. That is the absolute nature of the Supreme Personality of Godhead.

In Śrīmad-Bhāgavatam (10.39.44–57) it is stated that when Akrūra was accompanying Kṛṣṇa and Balarāma from Gokula to Mathurā, he entered the waters of the Yamunā River and could see all the planets of the spiritual sky. He also saw the Lord in His Viṣṇu form, as well as Nārada and the four Kumāras, who were worshiping Him. As stated in the Bhāgavata Purāṇa (Śrīmad-Bhāgavatam 10.40.7):

anye ca saṁskṛtātmāno
  vidhinābhihitena te
yajanti tvan-mayās tvāṁ vai
  bahu-mūrty-eka-mūrtikam

“The Supreme Lord’s many worshipers – the Vaiṣṇavas, or Āryans – are purified by the various processes of worship they perform according to their convictions and spiritual understanding. Each process of worship involves understanding different forms of the Lord, as mentioned in the scriptures, but the ultimate idea is to worship the Supreme Lord Himself.”

In His vaibhava-prakāśa feature, the Lord manifests Himself as Balarāma. The Balarāma feature is as good as Kṛṣṇa Himself, the only difference being that Kṛṣṇa’s bodily hue is blackish and Balarāma’s is whitish. The vaibhava-prakāśa form was also displayed when Kṛṣṇa appeared before His mother Devakī in the four-handed form of Nārāyaṇa, just when He entered the world. Then at the request of His parents He transformed Himself into a two-handed form. Thus He sometimes manifests four hands and sometimes two. The two-handed form is vaibhava-prakāśa, and the four-handed form is prābhava-prakāśa. In His personal form, Kṛṣṇa is just like a cowherd boy, and He thinks of Himself in that way. But when He is in the Vāsudeva form, He thinks of Himself as the son of a kṣatriya and feels like a kṣatriya, a princely administrator.

In His two-handed form as the cowherd son of Nanda Mahārāja, Kṛṣṇa fully exhibits His opulence, beauty, wealth, attractiveness and pastimes. Indeed, in some Vaiṣṇava literature it is found that sometimes, in His form as Vāsudeva, He becomes attracted to His form of Govinda in Vṛndāvana. Thus as Vāsudeva He sometimes desires to enjoy as Govinda does, although the Govinda form and the Vāsudeva form are ultimately one and the same. In this regard, there is a passage in the Lalita-mādhava (4.19), in which Kṛṣṇa addresses Uddhava as follows: “My dear friend, the form of this cowherd boy Govinda attracts Me. Indeed, I wish to be like the damsels of Vraja, who are also attracted by this form of Govinda.” Similarly, later in the Lalita-mādhava (8.34), Kṛṣṇa says: “Oh, how wonderful it is! Who is this person? After seeing Him, I am so much attracted that I now desire to embrace Him just like Rādhikā.”

There are also forms of Kṛṣṇa that are a little different from His original form, and these are called tad-ekātma-rūpa forms. These may be further divided into the vilāsa and svāṁśa forms, which in turn have many different features and can be divided into prābhava and vaibhava forms. As far as the vilāsa forms are concerned, there are innumerable prābhava-vilāsas, headed by Kṛṣṇa’s expansions as Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha. Sometimes the Lord thinks of Himself as a cowherd boy, and sometimes He thinks of Himself as Vasudeva’s son, a kṣatriya prince, and this “thinking” of Kṛṣṇa is called His “pastimes.” Actually, He is in the same form in His vaibhava-prakāśa and prābhava-vilāsa, but He appears differently as Kṛṣṇa and Balarāma. His expansions as Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha are the original catur-vyūha, or four-armed forms.

There are innumerable four-armed manifestations in different planets and different places. For instance, They are manifested in Dvārakā and Mathurā eternally. From the four original four-handed forms are manifested the twenty-four principal four-armed forms, which are called vaibhava-vilāsa. They are named differently according to the placement of the conch, club, lotus and disc in Their hands. The same four principal manifestations of Kṛṣṇa are found on each planet in the spiritual sky, known as Nārāyaṇa-loka or Vaikuṇṭha-loka. In Vaikuṇṭha-loka Kṛṣṇa is manifested in the four-handed form of Nārāyaṇa. From each Nārāyaṇa are manifested the forms of Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha. Thus Nārāyaṇa is the center, and the four forms of Vāsudeva, Saṅkarṣaṇa, Pradyumna and Aniruddha surround the Nārāyaṇa form. Each of these four forms again expands into three, and these all have different names, beginning with Keśava. These forms are twelve in all, and, again, They are known by different names according to the placement of the symbols in Their hands.

As far as the Vāsudeva form is concerned, the three expansions manifested from Him are Keśava, Nārāyaṇa and Mādhava. The three forms expanded from Saṅkarṣaṇa are known as Govinda, Viṣṇu and Śrī Madhusūdana. (It should be noted that this Govinda is not the same Govinda manifested in Vṛndāvana as the son of Nanda Mahārāja.) Similarly, from Pradyumna expand the three forms known as Trivikrama, Vāmana and Śrīdhara, and the three forms expanded from Aniruddha are known as Hṛṣīkeśa, Padmanābha and Dāmodara.