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The list of Dashavatara varies across sects and regions. The standard list is as follows: Matsya, Kurma, Varaha, Narasimha, Vamana, Parashurama, Rama, Krishna, Buddha, and Kalki. Sometimes, Krishna replaces Vishnu as the source of all avatars and Balarama takes Krishna's place in the list. In other versions, Krishna may be dropped from the list and substituted by regional deities like Vithoba, Jagannath or Balarama.
The order of the Dashavataras has been interpreted to be reflective of Darwinian evolution.
The word Dashavatara derives from daśa, meaning 'ten' and avatar (avatāra), meaning 'incarnation'.
Incarnation of the Divine
Restoration of the Divine
God Vishnu incarnates on Earth from time to time to eradicate evil forces, to restore the dharma and to liberate the worthy ones or devotees from the cycle of births and deaths. Vishnu in his avatar as Krishna speaks in the Bhagavad Gita, Chapter 4 Shloka 8: "To deliver the pious and to annihilate the miscreants, as well as to reestablish the principles of righteousness, I manifest myself, millennium after millennium".
A similar thread appears in Buddhism. The Pāli Canon refers to 28 Buddhas, while the Mahayana tradition additionally has many Buddhas of celestial origin, for example Amitābha and Vairocana. The Mahayana tradition also knows the Eighteen Arhats who protect the Buddhist faith, and all schools of Buddhism await for the coming of Maitreya, a buddha prophesied to arrive on earth many millennia after Gautama Buddha's death and nirvana.
The first four avatars of Vishnu appeared in Satya or Krita Yuga, the first of the four Yugas, also called 'The Golden Age', the next three in the second Yuga, the Treta Yuga, the two avatars after that appeared in the third Yuga, the Dwapara Yuga and tenth and last avatar will appear in the last Yuga, Kali Yuga. The time till completion for Kali Yuga is in 427,000 years. In the Vishnu Purana and the Bhagavata Purana, the Kali-yuga is described as ending with the appearance of Kalki, who will defeat the wicked, liberate the virtuous, and initiate a new Satya or Kalki Yuga.
At that time, the Supreme Personality of Godhead will appear on the earth. Acting with the power of pure spiritual goodness, He will rescue eternal religion. Lord Viṣṇu — the Supreme Personality of Godhead, the spiritual master of all moving and nonmoving living beings, and the Supreme Soul of all — takes birth to protect the principles of religion and to relieve His saintly devotees from the reactions of material work.— Bhagavata Purana, 12.2.16-17
- Matsya, the fish, from the Satya Yuga. Vishnu takes the form of a fish to save Manu from the deluge (Pralaya), after which he takes his boat to the new world along with one of every species of plant and animal, gathered in a massive cyclone.
- Kurma, the tortoise, from the Satya Yuga. When the devas and asuras were churning the Ocean of milk in order to get Amrita, the nectar of immortality, the mount Mandara they were using as the churning staff started to sink and Vishnu took the form of a tortoise to bear the weight of the mountain.
- Varaha, the boar, from the Satya Yuga. He appeared to defeat Hiranyaksha, a demon who had taken the Earth, or Prithvi, and carried it to the bottom of what is described as the cosmic ocean(much like in ether theory) in the story. The battle between Varaha and Hiranyaksha is believed to have lasted for a thousand years, which the former finally won. Varaha carried the Earth out of the ocean between his tusks and restored it to its place in the universe.
- Narasimha, the half-man/half-lion, from the Satya Yuga. The rakshasa (Demon) Hiranyakashipu, the elder brother of Hiranyaksha, was granted a powerful boon from brahma, not allowing him to be killed by man or animal, inside or out, day or night, on earth or the stars, with a weapon either living or inanimate. Vishnu descended as an anthropomorphic incarnation, with the body of a man and head and claws of a lion. He then disembowels the rakshasa at the courtyard threshold of his house, at dusk, with his claws, while he lay on his thighs.
- Vamana, a dwarf, from the Treta Yuga. The fourth descendant of Hiranyakashyap, Bali, with devotion and penance was able to defeat Indra, the god of firmament. This humbled the other deities and extended his authority over the three worlds. The gods appealed to Vishnu for protection and he descended as a boy Vamana. During a yajna (यज्ञ) of the king, Vamana approached him and Bali promised him for whatever he asked. Vamana asked for three paces of land. Bali agreed, and the dwarf then changed his size to that of a giant. He stepped over heaven in his first stride, and the netherworld with the second. Bali realized that Vamana was Vishnu incarnate. In deference, the king offered his head as the third place for Vamana to place his foot. The avatar did so and thus granted Bali immortality. Then in appreciation to Bali and his grandfather Prahlada, Vamana made him ruler of Pathala, the netherworld.
- Parashurama, warrior with the axe, from the Treta Yuga. He is son of Jamadagni and Renuka and received an axe after a penance to Shiva. He is the first Brahmin-Kshatriya in Hinduism, or warrior-saint, with duties between a Brahmin and a Kshatriya. King Kartavirya Arjuna and his army visited the father of Parashurama at his ashram, and the saint was able to feed them with the divine cow Kamadhenu. The king demanded the cow, but Jamadagni refused. Enraged, the king took it by force and destroyed the ashram. Parashurama then killed the king at his palace and destroyed his army. In revenge, the sons of Kartavirya killed Jamadagni. Parashurama took a vow to kill every Kshatriya on earth twenty-one times over, and filled five lakes with their blood. Ultimately, his grandfather, rishi Rucheeka, appeared before him and made him halt. He is a Chiranjivi (immortal), and believed to be alive today in penance at Mahendragiri.
- Rama, the prince and king of Ayodhya, from the Treta Yuga. He is a commonly worshiped avatar in Hinduism, and is thought of as the ideal heroic man. His story is recounted in one of the most widely read scriptures of Hinduism, the Ramayana. While in exile from his own kingdom with his brother Lakshman and the God Hanuman, his wife Sita was abducted by the demon king of Lanka, Ravana. He travelled to Lanka, killed the demon king and saved Sita.
- Krishna was the eighth son of Devaki and Vasudev, from the Dwapara Yuga. He is also a frequently worshiped deity in Hinduism and an avatar in Vaishnava belief. He appeared alongside his elder brother Balarama. Balarama is regarded generally as an avatar of Shesha. However, Balarama is included as the eighth avatar of Vishnu in the Sri Vaishnava lists, where Buddha is omitted and Krishna appears as the ninth avatar in this list. He may be particularly included in the lists, in circumstances where Krishna is removed and becomes the source of all avatars.
- '"Venkatesha"',from the Kali Yuga, is generally included as an avatar of Vishnu in Hinduism. His main abode is in Tirumala. He had taken this avatar to fulfill a devotee's wish to be married with him. He also took this avatar to be on Earth till the end of Kali Yuga.
- Kalki ("Eternity", or "White Horse", or "Destroyer of Filth"), will be the final incarnation of Vishnu, foretold to appear at the end of Kali Yuga, our present epoch. He will be atop a white horse and his sword will be drawn, blazing like a comet. He is the harbinger of end time in Hindu eschatology, and will destroy all unrighteousness and evil at the end of Kali Yuga.
The evolution of historical Vishnuism produced a complex system of Vaishnavism, often viewed as a synthesis of the worship of Vishnu, Narayana, Vasudeva and Krishna, and which was well established by the time of the Bhagavad Gita from 3138 BCE to the 3rd century CE.
Various versions of the list of Vishnu's avatars exist. Some lists mention Krishna as the eighth avatar and the Buddha as the ninth avatar, while others, such as the Yatindramatadipika, a 17th-century summary of Srivaisnava-doctrine, state Balarama as the eighth avatar and Krishna as the ninth.
The adoption of Buddha as one of the avatars of Vishnu under Bhagavatism was a catalyzing factor in assimilation during the Gupta period between 330 and 550 CE. By the 8th century CE, the Buddha was declared an avatar of Vishnu in several Puranas. The mythologies of the Buddha and Vishnu share a number of structural and substantial similarities, which contributed to the assimilation of the Buddha as an avatar of Vishnu. This assimilation is indicative of the Hindu ambivalence toward the Buddha and Buddhism. Conversely, Vishnu has also been assimilated into Sinhalese Buddhist culture, and Mahayana Buddhism is sometimes called Buddha-Bhagavatism. By this period, the concept of Dashavatara was fully developed.
In Maharashtra and Goa, Vithoba's image replaces Buddha as the ninth avatar of Vishnu in some temple sculptures and Hindu astrological almanacs. In certain Oriya literary creations from Orissa, Jagannath has been treated as the Ninth avatar, by substituting Buddha.
Status of Krishna
Srimanta Sankardeva considered Krishna as Vishnu himself, the source of all incarnations. Thus, in his Soturbinxoti Ovotar (Chaturvinshati Avatar) of the Kirttan Puthi, Krishna is not included, but Balarama is included.
In traditions that emphasize the Bhagavata Purana, Krishna is the original Supreme Personality of Godhead, from whom everything else emanates. Gaudiya Vaishnavas worship Krishna as Svayam Bhagavan, or source of the incarnations. The Vallabha Sampradaya and Nimbarka Sampradaya, (philosophical schools) go even further, worshiping Krishna not only as the source of other incarnations, but also Vishnu himself, related to descriptions in the Bhagavata Purana. Mahanubhavas also known as the Jai Kishani Panth, considers Lord Krishna as the supreme God and don't consider the list of Dashavatara while consider another list of Panchavatara (5 Avatars). 
Some modern interpreters sequence Vishnu's ten main avatars in a definitive order, from simple life-forms to more complex, and see the Dashavataras as a reflection, or a foreshadowing, of the modern theory of evolution. Such an interpretation was first propounded by Theosophist Helena Blavatsky in her 1877 opus Isis Unveiled, in which she proposed the following ordering of the Dashavataras:
- Matsya - fish, the first class of vertebrates; evolved in water(Indicates origin of Fishes in Silurian Period
- Kurma - amphibious (living in both water and land; but not to confuse with the vertebrate class amphibians)(Indicates origin of Amphibians in Devonian Period
- Varaha - mammals, wild land animals (Indicates Mammals origin in Triassic Period
- Narasimha - beings that are half-animal and half-human (indicative of emergence of human thoughts and intelligence in powerful wild nature)
- Vamana - short, premature human beings
- Parasurama - early humans living in forests and using weapons
- Rama - humans living in community, beginning of civil society
- Krishna - humans practicing animal husbandry, politically advanced societies
- Buddha - humans finding enlightenment
- Kalki - advanced humans with great powers of destruction.
This interpretation was taken up by other Orientalists and by Hindus in India, particularly reformers who sought to harmonize traditional religion with modern science. Keshub Chandra Sen, a prominent figure in the Brahmo Samaj and an early teacher of Swami Vivekananda, was the first Indian Hindu to adopt this reading. In an 1882 lecture he said:
The Puranas speak of the different manifestations or incarnations of the Deity in different epochs of the world history. Lo! The Hindu Avatar rises from the lowest scale of life through the fish, the tortoise, and the hog up to the perfection of humanity. Indian Avatarism is, indeed, a crude representation of the ascending scale of Divine creation. Such precisely is the modern theory of evolution.
Similarly, Monier Monier-Williams wrote "Indeed, the Hindus were ... Darwinians centuries before the birth of Darwin, and evolutionists centuries before the doctrine of evolution had been accepted by the Huxleys of our time, and before any word like evolution existed in any language of the world." J. B. S. Haldane suggested that Dashavatara gave a "rough idea" of vertebrate evolution: a fish, a tortoise, a boar, a man-lion, a dwarf and then four men (Kalki is not yet born). Nabinchandra Sen explains the Dashavatara with Darwin's evolution in his Raivatak. C. D. Deshmukh also remarked on the "striking" similarity between Darwin's theory and the Dashavatara.
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