The primary meaning of the term Avatāra is derived from avataraṇa, that is, to come down. God comes down to earth, assuming a different form, from his celestial abode — this is the avatāra or avataraṇa (incarnation) of God. The huge gap between the worldly abode of mankind and the distant antarīkṣaloka seems to be wiped out, by the grace of this ‘coming down’ of God. Above all, he comes down to rescue and redeem the suffering humanity, people in pain and trouble. The conceptualisation of a redeeming Deity was not only prevalent in India, but elsewhere in the ancient civilisation also. A scholar has noted —
“The saviour is an essential factor in religion, because many religious people are convinced that the domain of men and the world of gods are separated by a deep cleft. In order to link up these two worlds a bridge must be laid across the cleft. Man is unable to perform this act. It should be done by a creature who unites these two worlds by his nature. That is the saviour. He is a divine or semi-divine being, who descends from from the domain of the gods to the dwelling places of man, or who operates through other gods for the benefit of men. The figure of the saviour shows many varieties. As he combines in  Himself a human and a divine element, the emphasis may alternatively be must on the one or the other side of his nature. Saviours, in whom the human factor dominates, are the sacral king, the hero the prophet, the sage and the saint.

There have been various research works on the Avatāra-conception in India, and it is also clear from that great sages or kings, great learned people are also considered as possessing the vibhūti (vibhuti; divine grace) of God. They also act as a saviour or redeemer, but they are not ‘avatāra’ in the true sense of the term, but they are avatāra-like. The proposition laid by Bhagavadgītā is very important — The power and grace of God exist in persons or things who/that possess great beauty, great power or some special attributes or influence of the highest level —
yad yad vibhūtimat sattvaṃ śrīmadūrjitameva vā
tattadevāgaccha tvaṃ mama tejo’sambhavam.

These great people, religious teachers, sages or prophets, and even gurus are considered avatāra-like, because they guide and redeem the common people. They act as a divine’link’ or ‘mediator’ between the worldly human beings and God the Almighty —

“The name guru is applied to a man of any caste who is believed to be in peculiarly  close communion with the Highest Being or Supernatural power and to hold the secret of divine mysteries, whether on account of asceticism, utterances regarded as inspired, or saintliness of life and character. The basis of he peculiar veneration of the guru still lies in the conviction that he is a link in a long chain of transcendental beginnings, a mediator agle to bring his disciple and God together, or a medium through whom God is willing to reveal himself. Those who on account of their highly developed spirituality and earnest religious life need no guru are rare. Gandhi wrote, ‘I believe in the Hindu theory of guru and his importance in spiritual realisation. I think there is a great deal of truth in the doctrine that true knowledge is impossible without a guru. Only a perfect jnani (on who having spiritual knowledge knows the path to Release) deserves to be enthroned a guru. Most of those who want to reach God must follow such a guide, who is no mere man, but a ‘channel through which Gods communicates Himself to the adept’. Hence the conviction that the guru alone can guide his disciples on the path of spiritual progress to full knowledge of the highest  which leads to ultimate emancipation. Thus he is, to the present day, a Respektsperson’, performing various functions and entering into different relations to the adherents.”

The difference between great people, sages , prophets or gurus and Avatāra(s) is that, in Indian faith, God Himself, or assuming some form(s) descends on earth to destroy evil and to bestow his grace on humanity for the benefit of humankind. The true purpose of God’s incarnation is clearly stated in two well-known śloka(s) of Bhagavadgītā. There God is saying, “Whenever there is decay of righteousness, that is, Dharma, and there is exaltation of unrighteousness, then I Myself come forth ; For the protection of the good, for the destruction of evil-doers, For the sake of firmly establishing righteousness, I manifest myself through ages (from age to age).”

yadā yadā hi dharmasya glānirbhavati bhārata
abhyutthānamadharmasya tadātmānam sṛjāmyaham.
paritrāṇāya sādhūnām vināśāya ca duṣkṛtām
dharmasaṃthāpanārthāya sambhavāmi yuge yuge.

Dharma here means an overall prevalance of righteousness in social political and other spheres of life, and Adharma is the decline of this order, and growth of evil, corruption, injustice, or whatever is anatagonistic to the virtuous or the good, as symbolised by Asura, Daitya or Demons.  In Saptaśatī Candī (Saptasati Chandi) of Mārkaṇḍeyapurāṇa (Markandeyapurana), this purpose of assuming incarnation is also stated. There goddess Caṇḍī says, “Whenever there is rise of the demons and they create damage to this world, I descend to destroy the enemies —
itthaṃ yadā yadā vadhā dānavotthā bhaviṣyati
tadā tadāvatīryāhaṃ kariṣyāmyarisaṃkṣayam. 

In the Avatāra-conceptualisation of India, the purpose of relieving the earth of its burden, destroying the evil and preserving the good becomes the prominent one, and in several Purāṇa(s) it is found that Goddess Earth, assuming the form a cow, seeks protection from Brahmā at first, and then Viṣṇu.

bhūmirdṛpto nṛpavyāja daityānikaśatayutaiḥ
ākrāntā bhūribhāreṇa brahmāṇa śaraṇaṃ yayau.
gaurbhūtvāśrumukhī khinna krandantī karuṇaṃ vivhoḥ
upasthitāntike tanme vyasanaṃ samavocata.

In fact, Goddess Earth or Bhūdevī (Bhudevi) has also been hailed as a wife of God Viṣṇu — Bhūrvaiṣṇavī (Bhurvaishnavi), Mādhavī (Madhavi) Devi in Rāmāyaṇa  (Ramayana) — tathā me mādhavī devī vivaraṃ dātumarhati . At the time of Sīta’s desecnt into the earth, she has become one and unified with Mādhavī or Goddess Lakṣmī, that is, Bhūdevī has been identified with Śrīdevī (Sridevi). In Mahābhārata-Purāṇa (Mahabharata-purana), Bhūdevī or Goddess Earth is the second wife of Viṣṇu, after Lakṣmī. In Śrīsūkta (Srisukta), however, the Earth-Goddess is directly referred to as the wife of Viṣṇu — viṣṇupatnīṃ kṣamāṃ deviṃ.

Both Kṣhamā (Kshama) and Kṣmā (Kshma) means ‘the Earth; and she is is conceptualised as the wife of Viṣnu. It is because of this close association, it is not surprising that Viṣṇu will assume incarnations to take away the ‘burdens’ of the earth – whereas executing the preservation of the virtuous and retribution for the sinners, becomes his secondary purpose.

nṛloke daśa janmāni lapsyase madhusūdanaḥ
bhāryāste viyogena duḥkhānyanubhaviṣyasi.

The ten births of Viṣṇu mean the ten incarnations of Viṣṇu. The Bhūmikhaṇḍa of Padmapurāṇa also mentions the ten avatāra(s) of Viṣṇu, due to the curse of Bhṛgu, the legend there is very different. Here Bhṛgu was performing a yajña. Viṣṇu promised that he would protect the yajña. Now, a terrible war broke out between gods and demons, and at Indra’s insistent request, Viṣṇu had to go to help them. Though he promised Bhṛgu, he went away leaving the place —
indrasya vacanāt sadyo gato’sau dānavaiḥ saha
yoddhuṃ vihāya govindo bhṛgoścaiva makhottatam.
The gods invited to the yajña left it, and Viṣṇu too, without keeping his promise went along with them. Seeing this, the demons ruined Bhṛgu’s yajña. Bhṛgu then cursed him —
daśa janmāni bhunkṣa tvam macchāpakluṣīkṛtaḥ.
karmaṇaḥ svasya sambhogaṃ sambhokṣyati janārdanaḥ.
That is, Viṣṇu will have to bear the consequence of his fault. Tainted with my curse, he will have to take births ten times in satyaloka.

In Bhūmikhaṇḍa of Padmapurāṇa, there is mentioned that the gods’ mother, Aditi was also incarnated along with Viṣṇu. Once Viṣṇu, accompanied by gods, came to visit Aditi. He wished to grant her a boon. Aditi said, “By your grace, I have got the immortal gods as my sons. But now I would like to have you as my son. Then Viṣṇu said to her, “When you will assume a human form in order to serve some divine cause, I shall be born as your son.In this context, Viṣṇu mentioned his incarnations as Paraśurāma, Dāśarathi Rāma and Vāsudeva Kṛṣṇa.

Scholars speak of some further purposes behind assuming incarnation, and these purposes sometimes, become so important that the primary purposes become secondary. It is to be noted that in the context of God Viṣṇu’s incarnation, this has become established that Rescuing dharma from decline and bringing retribution upon evil is a sādhāraṇa karma of God Viṣṇu, for this, he does not need to take incarnations. God’s own purposes are also fulfilled by assuming human incarnations. In case of Rāmacandra-avatāra, this can be applied with a proper validity. In this context, Bankimcandra Chattopadhyay has said, “Human being egagae themselves in deeds, pressed by the need for self-protection and several attributes, but such deeds as are beneficial to the holistic development, harmony and fulfilment of all attributes, are difficult to execute. For that, one needs an ideal. There is nobody except God himself, who can be the complete ideal of holistic dharma…
If God himself takes a quiet human form and appears in front of people, the ideal he sets can really be beneficial for the development of dharma. Man is ignorant of karma, he does not know how karma can be executed in accordance with dharma; there is a good possibility of learning that lesson if God himself asssumes an incarnation. So, it is impossible that God, out of compassion to mankind, will assume incarnations [to such ideals to human beings?] An ‘Avatāra’ must establish a high ideal before all humankind — this notion became very important for Bankimcandra. Just slaying some Rāvaṇ-Kumbhakarṇa or Kaṃsa-Śiśupāla, according to him, was not at all a respectful purpose. The duty of a divine incarnation is to establish an ideal. We would, however, say that this argument is well applicable to Rāma, but the character of Kṛṣṇa is very complicated. However much of an idealistic leader or the ‘Bismark of Mahābhārata’ Kṛṣṇa might have been, in Bankim’s conception, he is after all not the complete Kṛṣṇa. There are philosophers who must contradict Bankim’s point, and in that argument Bankim’s defeat was inevitable, and that was why he did not step into that side, consciously. We would, however, say that this argument is well applicable to Rāma, but the character of Kṛṣṇa is very complicated. However much of an idealistic leader or the ‘Bismark of Mahābhārata’ Kṛṣṇ might have been, in Bankim’s conception, he is after all not the complete Kṛṣṇa. There are philosophers who must contradict Bankim’s point, and in that argument Bankim’s defeat was inevitable, and that was why he did not step into that side, consciously.

The philosopher would say — the purpose of assuming human Avatāra is not only slaying one Rāvaṇa or a Kaṃsa, nor even establishing a big ideal in front of humankind. There is God’s own interest working behind. And there is the great poet, he will also say — God is ever-free, so he takes delight in being bound, and we are already in bounds, so we seek freedom. That is why He, being Lord of the Lords, comes down to play in intimacy with us — for Himself, as well as for ourselves.

Since all religions in India are founded upon the base of Philosophy, it is not possible to leave out the fundamental premise of the philosophers. Pointing at the ancient utterance of Vṛhadāraṇyaka Upaniṣad — the Ekamevādvitīyam Puruṣa of Upaniṣad was bored out of being alone, there was no pleasure in his mind —
sa vai naiva reme, yasmad ekākī na ramate.

Pleasure cannot be obtained alone. So He became jāyā dividing himself into two. It is not only a matter of destroying monsters and demons, or establishing an ideal , rather more important than that. Though the cycles of birth and death cannot touch him — ajo’pi san avyayātmā, he took birth. Being the lord of all bhūtas, — bhūtānāmīśvaro’pi san — he came to be bound in the illusions of worldly pleasure and pains common to human life.

In this way, he becomes subject to pleasure and pain. Philosophers with a connoisseur’s mentality would call it līlā. The term is not simple, because through this term only, the humanlike activities of God can be explained. Brahmasūtra has written that the creation of this world is a product of God’s līlā —
lokavattu līlākaivalyam.

So, if God comes to play for sometime in his own playhouse, to enjoy his līlā, the philosopher takes delight in this. But the historian does not take pleasure, he does not care about such līlā-activities. We would say, there is no problem in that, too. The is no wonder that the historian would him a man — One who is tranformed from man to god, in Upaniṣad, Purāṇa, Rāmāyaṇa. In the view of a historian, Rāmāyaṇa ends in five kāṇḍa(s). They believe only in the humanity of Rāma. In a historian’s perspective, Rāmāyaṇa has started with the internal conflicts of the royal house of Ayodhyā, and it ends with the rescue of Sītā, after winning the battle of Laṅkā. But through Rāma’s youth, marriage, self-sacrifice, many trials of living in exile and finally his victory over the Rākṣasa(s) — the historian ultimates reaches at his humanity, what Parinder has described as follows – “all make up a human being”. A philosopher, though already recognising the fundamentally divine self of Rāma, finally aim at his humanity. But the difference between the two is that — one (the historian) considers Rāma as a human being from the very beginning, and he thinks that Rāma had been identified with God Viṣṇu because of Indian people’s tendency to worship a person as an icon. The other, that is, thae phisosopher knows Rāma as a manifestation of God Viṣṇu from the beginning, but he has been behaving like a human being in course of his līlā. All his deeds, actions — whether righteous or wrong — are done as part of his līlā.

Since both for the historian and the philosopher, the establishment of God’s humanity is the fundamental purpose, we can reach Kṛṣṇa starting from Rāmacandra, though both historicity and philosophy have been too complicated in the life-discourse of Kṣṇ, or in the analisis of his character. First, Vyāsa’s Mahābhārata is not the only element, there are so many Purāṇ-legends which have led him further away from Mahābhārata. Second, the main purpose of assuming Avatāra- that is, destroying the evil and preserving the virtuous — has become secondary in case of Kṛṣṇa. Even, according to Bankimchandra, if the establishment of an high ideal becomes the purpose of Kṛṣṇ-avatāra, still from a historical perspective, Kṛṣṇa is very different.

In the deeper conceptualisation of Avatāra-theory, Rāmacandra has been discussed at length, and Kṛṣṇa has been discussed in further details. As Bankimcandra has thought, in order to teach a lesson of leading an ideal-life, God has to assume Avatāra, and in this regard, Rāmacandra can be the only ideal. So it is said that Rāma’s ways are to be followed, not that of Rāvaṇa’s.

rāmādivat pravartitavyāṃ na tu rāvaṇādivat.

However, if, in case of Rāma, the establishment of an idea turns out to be an extra, ulterior motif -o other than relieving the world of its burden, in Kṛṣṇa-avatāra it creates a deeper philosophical motif. It is expressed very nicely in Bhāgavatapurāṇa. After the battle of Kurukṣetra, when Kṛṣṇa was returning from Hastināpura (Hastinapura) to Dvāraka, Kuntī sang his praise by saying that — “Your true self is beyond our knowledge, yet you incarnate yourself to define Bhaktiyoga for pure-minded Parmahaṃsa sages; how can ordinary women like us realise you —
tathā paramahaṃsānāṃ munīnāṃ amalātmanām
bhaktiyoga-vidhānārthaṃ kathaṃ paśyema hi striyaḥ.
The bhakti mentioned here is not only synonymous to dependence upon or allegiance to God, it is premabhakti. Elaborating upon this thought, Rūpagosvāmi, an ardent associate of Śrī Caitanya, has written in his Laghubhāgavatāmṛta (Laghubhagavatamrita)– there are so many other incarnations of God, and all of them have worked for the holistic benefit of humankind , but Śrī Kṛṣṇa perhaps is the only one, who has showered his divine love even upon plants and creepers.
sambhavatārā vahavaḥ puṣkaranābhasya sarvtobhānaḥ
kṛṣṇādanyā ko vā latāsvapi premado bhavati.

Whether it is determining premabhakti, as stated by Kuntī, or for bestowing his divine love, as expressed buy Rūpagosvāmi, is the jagatsamvandhī kāraṇa (world-related cause) of Kṛṣṇa’s assuming Avatāra. Generally, it is out of his mercy to the human world, that he assumes incarnations. But in case of Kṛṣṇāvatāra, there is a further, deeper cause of his being incarnated — other than these worldly causes, as the Vaiṣnava philosophers would say.

Here, at first, they refer to the utterance of Akrūra as a proof. Akkrūra was then coming from Mathurā to Vṛndāvana to take Kṣṇa to Mathurā. On his way, among his manyother thoughts, he said once — the Lord of the universe, in order to execute some work lying in his heart, has assumed a human body at his own will —
sāmpratañca jagatsvāmī kāryamātmahṛdisthitam
kartuṃ manuṣyatāṃ prāptaḥ svecchādehadhṛgavyayam.

The Vaiṣnava philosophers think that God himself is Rasasvarūpa, but it is not possible, being the only and one, to taste one’s own self. So, in order to enjoy that divine rasa, and to let his assiciates enjoy the same, He has taken a human form in the shape of Kṛṣṇa. In Bhāgavata-purāṇa Brahmā once said, there is no other reason of your assuming a human form. You have done this, to enjoy your own pastime-pleasure, that is called līlā —
na te bhavasyeha bhavasya kāraṇam
vinā vinodaṃ vata tarkayamahe.

In this self-enjoyment-conceptualisation of Bhāgavatapurṇa , we have a resonance of the utterance of Vṛhadāraṇyaka Upaniṣad — sa vai naiva reme. yasmādekākī na ramate. This utterance leaves aside God’s Ātmārāma-vṛtti

ete cānye ca vahavo divyā devagunairyutāḥ
prādurbhāvāḥ purāṇeṣu gīyante brahmavādibhiḥ.
etaduddeśamatreṇa prādurbhāvānukīrtanam
kīrtitaṃ kīrtanīyasya sarvalokaguroḥ prabhoḥ.

Scholars think that in Mahābhārata, the theory of Avatāra has not been developed properly. In the previously mentioned śloka(s) of Śāntiparva, there has been a list of Avatāra(s), and except that Kṛṣṇa, Valarāma, Dāśarathi Rāma, Vāmana, Varāha and Narasiṃha. Among them, Narasiṃha and Vāmana are referred to briefly, however, for Varāha, a full chapter is allotted in Śāntiparva, and Dāśarathi Rāma has received some importance in the Rāmopakhyāna delivered by Mārkaṇḍeyamuni. Still, the act of assuming Avatāra and its significance is not discussed in Mahābhārata in great detail. Rather such matters have been more important in Harivaṃśa, Viṣṇupurāṇa or Bhāgavatapurāṇa.

From chapter two to sixteen in Agnipurāṇa (Agnipurana), the characteristics of several Avatāra(s) — from Matsya to Kalki — have been described in datails. Matsya, Kūrma and Varāha have been given some elaboration, but Nṛsiṃha, Vāmana and Paraśurāma have been described very briefly. But the description of Rāma-avatāra covers more than one chapters, so is that of Kṛṣṇ. . Both Buddha and Kalki are mentioned here as Avatāra. It is also to be noted that in Agnipurāṇa, though the term ‘Daśāvatāra’ (Dasavatara) is mentioned, the innumerable numbers of Avatāra(s) been indicated, too — avatārā asaṃkhyātā atītāgaṇnādayaḥ.

In Varāhapurāṇa (Varahapurana), there is the clearest statement about the ten incarnations of Viṣṇu — Matsya, Kūrma, Varāha, Nṛsiṃha, Vāmana, Dāśrathi Rāmacandra, Kṛṣṇa and Paraśurāma, Kṛṣṇa, Buddha and Kalki — these ten Avatāra(s) —
matsyaḥ kūrmo varāhaśca narasiṃho’tha vāmanaḥ
rāmo rāmaśca kṛṣṇaśca buddhaḥ kalkī ca te daśa.
The speciality of Varāhapurāṇa is that, here Kṛṣṇa is included among the ten Avatāra(s), and Valarāma is excluded.

In Mārkaṇḍyapurāṇa the holistic self of God is conceptualised in terms of a spiritual division, and it is said that the tritīyā tanu (tritiya tanu; third aspect) of God protects the prajā (praja; the people), and this third aspect of God, full of His Sattvaguṇa   redeems the humankind at the time of the decay of Dharma and rise of Adharma.

tritīyā karma kurute prajāpālanatatparā
sattvoddriktātu sā jñeyā dharmasaṃsthānakāriṇī.

In the context of this dharmasaṃsthānakāriṇī tritiyā tanu, Kūrmapurāṇa (Kurmapurana) has but briefly mentioned Varāha, Nṛsiṃha, Vāmana, and said that there is no need to talk about so many Avatāra(s), they are all incarnations of the One who has now been born in Mathurā (Mathura).

vāmanādīṃstathaivānyān na sankhyātumihotsahe
avatārāṃśca tasyaiha māthuraḥ sāmprataṃ tvayam.

In Mārkaṇḍeyapurāṇa, however, Vāsudeva Kṛṣṇa is hailed as Avatāra-vīja or Avatārī.

In Brahmapurāṇa, discussions regarding Avatāra and the number of Avatāra(s) are similar to Harivaṃśa . Here, too, the presence of Matsya and Kūma has not been clearly described, and the śloka(s) are almost borrowed from Harivaṃśa. While naming the Avatāra(s), this Purāṇ briefly mentions Varāha, Vāmana, Dattātreya, Jāmadagnya Paraśurāma, Dāśarathi Rāma, Māthura (that is, Kṛṣṇa) and Kalkī. But like Harivaṃśa, Buddha is not mentioned here, and at the end of this list, there is the same vinaya-vākya, as in Harivaṃśa — ‘Just for the sake of references, some of the kīrtanīya prādurbhāva(s) have been mentioned, but there are more and more Avatāra(s) —
etaduddeśmātreṇa prādurbhāvānukīrtanam
kīrtitaṃ kīrtanīasya sarvalokagurorvibhoḥ .

Regarding the variety and variations of Avatāra-nāma, the number of Avatāra(s), and the purpose of assuming these Avatāra(s) — the most thoughtful discourses are found in Bhāgavatapurāṇa. But these thoughts are discussed with more scholarship and insight, by Rupagosvāmi, the ardent follower of Srī Caitanya and other devotees of him.

According to Bhāgavatapurāṇa, the number of Avatāra(s) is twenty two. The first Avatāra is that great being of Supreme Consciousness, as conceptualised by Sāṃkyadarśna, the great Puruṣa who manifests Himself through Triguṇā Prakṛti, through such vikāra(s) as Mahat-Ahaṃkāra –jagṛhe pauruṣaṃ rupaṃ bhagavān mahadādibhiḥ.
After the Puruṣa-form , there come the Kumāra-form, where Brahmā is established in the Brahmacarya of Brāhmaṇa. But even this Brahmā is a manifestation of the vaikārika form of the Prathama Prakṛti, so he is not an Avatāra beyond the Puruṣa-form. So the Śaukara-vapu Varāha is second Avatāra

In the beginning of Mahābhārata, there is one upaparva (sub-section) called Aśāvataraṇa. There it is said that the Kauravas, Pāṇḍava(s) and their all relations, all kings were partial incarnations of either some gods or some great demon. At one point in Mahābhārata itself, Kṛṣṇa and Valarāma are said to have been incarnated from the airs of God Nārāyaṇa. When the God picked up one black and one white hair from his head, and threw them away, the white one entered the womb of Rohiṇī, wife of Vasudeva, and the black one entered the womb of his second wife, Devakī. Thence emerged Valarāma and Kṛṣṇa.
dvau cāpi keṣau niviśetāṃ yadunāṃ
kūle striau rohiṇīṃ devakīñca
tayoreka valadevo vabhūva
kṛṣṇo dwitīyaḥ keśavaḥ samvavabhūva.
In Rāmāyaṇa, we have also seen that when God Viṣṇu, at the request of other gods, decided to take birth in the house of Daśratha, Brahmā asked the other gods to be born on earth as Vānara(s) to assist God Viṣṇu.
sṛsaddhaṃ harirūpeṇa putrāṃstulyaparākramān
Then we come to see that begগinning with Brahmā, Indra, Sūrya, Kuvera, Varuṇa, Viśvakarmā and Vāyu — all the gods took birth as Vānara(s). Likewise, in Bhāgavatapurāṇa, when Viṣṇu assumed his incarnation at the request of Brahmā and other gods, Brahmā also instructed the wives of the gods to take birth in the earthly abode, to please God Viṣṇu —
janiṣyate tatpriyārthaṃ sambhavavantu surstriyaḥ.

It is to be noted that whenever God Viṣṇu assumes an incarnation, his consort Śrī or Lakṣmī also incarnates herself to offer assistance in his līlā.

He instigated Viṣṇu to talk to Bhṛgu. Viṣṇu, having no other option, repeatedly asked Bhṛgu to return what belonged to his wife. Bhṛgu became so annoyed with this insistence of Viṣṇu, that he cursed him — you have to take birth ten times on earth, and suffer from separation with your wife —

Such is the popularity of the legend of God Viṣṇu’s ten incarnations, that Daśāvatāra-stotra (Dasavatara-stotra) in Jayadeva’s Gītagovindam (Gitagovindam) and the description of Viṣṇu’s ten incarnations in Daśavatāra-caritra by Kṣemendra (Kshemendra), have been famous –
matsyaḥ kūrmo varāhaḥ puruṣahari harivapurvāmano jāmadagnyaḥ
kākutsthyaḥ kaṃsahantā sa ca sugatamuniḥ karkināmā ca viṣṇuḥ.
It is to be noted that in the list given by Kṣemendra, there is no mention of Valarāma, but the Kaṃsa-slayer Kṛṣṇa is there; and in Daśāvatāra-stotra in Gītagovindam, there are Valarāma, Buddha and Kalki, but not Kṛṣṇa. Kṛṣṇa here is Avatāra-vīja, that is the seed or source of all other Avatāra(s) -keśava dhṛto daśvidharūpaḥ.

The ten incarnations emerge out of him, Kṛṣṇa here is Daśākṛtikṛt —
vedānnuddharate jaganti vahate bhūgolamudvijate
daityaṃ dārayate valiṃ chalayate kṣatrakṣayaṃ kurvvate.
paulastyaṃjayate halaṃkalayate kāruṇāmātaṅgate
mlecchān mūrcchayate daśākṛtikṛte kṛṣṇāya tubhyaṃ namo namaḥ.