An avatar (Sanskrit: अवतार, IAST: avatāra), a concept in Hinduism that means "descent", is the material appearance or incarnation of a deity on earth. The relative verb to "alight, to make one's appearance" is sometimes used to refer to any guru or revered human being.
The word avatar does not appear in the Vedic literature, however it appears in developed forms in post-Vedic literature, and as a noun particularly in the Puranic literature after the 6th century CE. Despite that, the concept of an avatar is compatible with the content of the Vedic literature like the Upanishads as it is symbolic imagery of the Saguna Brahman concept in the philosophy of Hinduism. The Rigveda describes Indra as endowed with a mysterious power of assuming any form at will. The Bhagavad Gita expounds the doctrine of Avatara but with terms other than avatar.
Theologically, the term is most often associated with the Hindu god Vishnu, though the idea has been applied to other deities. Varying lists of avatars of Vishnu appear in Hindu scriptures, including the ten Dashavatara of the Garuda Purana and the twenty-two avatars in the Bhagavata Purana, though the latter adds that the incarnations of Vishnu are innumerable. The avatars of Vishnu are important in Vaishnavism theology. In the goddess-based Shaktism tradition of Hinduism, avatars of the Devi in different appearances such as Tripura Sundari, Durga and Kali are commonly found. While avatars of other deities such as Ganesha and Shiva are also mentioned in medieval Hindu texts, this is minor and occasional. The incarnation doctrine is one of the important differences between Vaishnavism and Shaivism traditions of Hinduism.
Incarnation concepts similar to avatar are also found in Buddhism, Christianity, and other religions. The scriptures of Sikhism include the names of numerous Hindu gods and goddesses, but it rejected the doctrine of savior incarnation and endorsed the view of Hindu Bhakti movement saints such as Namdev that formless eternal god is within the human heart and man is his own savior.
The Sanskrit noun (avatāra ; Hindustani: [əʋˈtaːr]) is derived from the Sanskrit roots ava (down) and tṛ (to cross over). These roots trace back, states Monier-Williams, to -taritum, -tarati, -rītum. It's cognate to "away" in English, which is root from PIE *au- means "off, away". 
Avatar literally means "descent, alight, to make one's appearance", and refers to the embodiment of the essence of a superhuman being or a deity in another form. The word also implies "to overcome, to remove, to bring down, to cross something". In Hindu traditions, the "crossing or coming down" is symbolism, states Daniel Bassuk, of the divine descent from "eternity into the temporal realm, from unconditioned to the conditioned, from infinitude to finitude". An avatar, states Justin Edwards Abbott, is a saguna (with form, attributes) embodiment of the nirguna Brahman or Atman (soul).
Neither the Vedas nor the Principal Upanishads ever mention the word avatar as a noun. The verb roots and form, such as avatarana, do appear in ancient post-Vedic Hindu texts, but as "action of descending", but not as an incarnated person (avatara). The related verb avatarana is, states Paul Hacker, used with double meaning, one as action of the divine descending, another as "laying down the burden of man" suffering from the forces of evil.
The term is most commonly found in the context of the Hindu god Vishnu. The earliest mention of Vishnu manifested in a human form to establish Dharma on Earth, uses other terms such as the word sambhavāmi in verse 4.6 and the word tanu in verse 9.11 of the Bhagavad Gita, as well as other words such as akriti and rupa elsewhere. It is in medieval era texts, those composed after the sixth century CE, that the noun version of avatar appears, where it means embodiment of a deity. The idea proliferates thereafter, in the Puranic stories for many deities, and with ideas such as ansha-avatar or partial embodiments.
The term avatar, in colloquial use, is also an epithet or a word of reverence for any extraordinary human being who is revered for his or her ideas. In some contexts, the term avatara just means a "landing place, site of sacred pilgrimage", or just "achieve one's goals after effort", or retranslation of a text in another language. The term avatar is not unique to Hinduism even though the term originated with hinduism. It is found in the Trikaya doctrine of Mahayana Buddhism, in descriptions for the Dalai Lama in Tibetan Buddhism, and many ancient cultures.
The manifest embodiment is sometimes referred to as an incarnation. The translation of avatar as "incarnation" has been questioned by Christian theologians, who state that an incarnation is in flesh and imperfect, while avatar is mythical and perfect. The theological concept of Christ as an incarnation, as found in Christology, presents the Christian concept of incarnation. According to Oduyoye and Vroom, this is different from the Hindu concept of avatar because avatars in Hinduism are unreal and is similar to Docetism. Sheth disagrees and states that this claim is an incorrect understanding of the Hindu concept of avatar.[note 1] Avatars are true embodiments of spiritual perfection, one driven by noble goals, in Hindu traditions such as Vaishnavism.
The concept of avatar within Hinduism is most often associated with Vishnu, the preserver or sustainer aspect of God within the Hindu Trinity or Trimurti of Brahma, Vishnu and Shiva. Vishnu's avatars descend to empower the good and fight evil, thereby restoring Dharma. Traditional Hindus see themselves not as "Hindu", but as Vaishnava (Worshippers of Vishnu), Shaiva (Worshippers of Shiva), or Shakta (Worshipper of the Shakti). Each of the deities has its own iconography and mythology, but common to all is the fact that the divine reality has an explicit form, a form that the worshipper can behold. An oft-quoted passage from the Bhagavad Gita describes the typical role of an avatar of Vishnu:
Whenever righteousness wanes and unrighteousness increases I send myself forth.
For the protection of the good and for the destruction of evil,
and for the establishment of righteousness,
I come into being age after age.
The Vishnu avatars appear in Hindu mythology whenever the cosmos is in crisis, typically because the evil has grown stronger and has thrown the cosmos out of its balance. The avatar then appears in a material form, to destroy evil and its sources, and restore the cosmic balance between the ever-present forces of good and evil.
The most known and celebrated avatars of Vishnu, within the Vaishnavism traditions of Hinduism, are Krishna, Rama, Narayana and Vasudeva. These names have extensive literature associated with them, each has its own characteristics, legends and associated arts. The Mahabharata, for example, includes Krishna, while the Ramayana includes Rama.
The Bhagavata Purana describes Vishnu's avatars as innumerable, though ten of his incarnations (Dashavatara), are celebrated therein as his major appearances. The ten major Vishnu avatars are mentioned in the Agni Purana, the Garuda Purana and the Bhagavata Purana;
The ten best known avatars of Vishnu are collectively known as the Dasavatara (a Sanskrit compound meaning "ten avatars"). Five different lists are included in the Bhagavata Purana, where the difference is in the sequence of the names. Freda Matchett states that this re-sequencing by the composers may be intentional, so as to avoid implying priority or placing something definitive and limited to the abstract.
The Bhagavata Purana also goes on to give an alternate list, wherein it numerically lists out 22 Vishnu avatars in chapter 1.3.
Avatars like Hayagriva, Hamsa and Garuda are also mentioned in the Pañcaratra making the total of thirty-nine avatars. However, despite these lists, the commonly accepted number of ten avatars for Vishnu was fixed well before the 10th century CE.
The avatar concept was further developed and refined in later Hindu texts. One approach was to identify full avatar and partial avatars. Krishna, Rama, and Narasimha were full avatars (purna avatars), while others were partial avatars (ansha avatars). Some declared, states Noel Sheth, that every living creature is an avatar of Vishnu. The Pancharatra text of Vaishnavism declares that Vishnu's avatar include those that are direct and complete (sakshad), indirect and endowed (avesha), cosmic and salvific (vyuha), inner and inspirational (antaryamin), consecrated and in the form of image (archa).
Yet another classification, developed in Krishna schools, centers around Guna-avatars, Purusha-avatars and Lila-avatars, with their subtypes. The Guna-avatar classification of avatars is based on the Guṇas concept of the Samkhya school of Hindu philosophy, that is Rajas (Brahma), Sattva (Vishnu), and Tamas (Shiva). These personalities of the Trimurti are referred to as Guna avatars. The Purushavatara are three. The first evolves the matter (Prakriti), the second is the soul present in each individual creature, the third is the interconnected oneness or Brahman that connects all souls. The Lilavataras are partial or full manifestations of Vishnu, where either some powers (Shakti) or material parts of him exist.
Vishnu is Purushavatara. The Matsya, Kurma, and Vamana avatars of Vishnu are Lilavataras. A Purnarupa in this classification, is when Vishnu manifests completely along with his qualities and powers. In Bengal Vaishnavism, Krishna is the Purnarupa. In Shaivism, Bhairava is the purnarupa of Shiva.
Dasam Granth has three major compositions, one each dedicated to avatars of Vishnu (Chaubis avatar) and Brahma. However, Sikhism rejects the doctrine of savior incarnation, and only accepts the abstract nirguna formless god. The Sikh Gurus endorsed the view of Hindu Bhakti movement saints such as Namdev (≈1270 – 1350 CE) that formless eternal god is within human heart and man is his own savior.
The Linga Puranam declares that Ganesha incarnates to destroy demons and to help the gods and pious people. The two upapuranas – Ganesha Purana and Mudgala Puranam – detail the avatars of Ganesha. Both these upapuranas are core scriptures of the Ganapatya sect – exclusively dedicated to Ganesha worship.
Four avatars of Ganesha are listed in the Ganesha Purana: Mohotkata, Mayūreśvara, Gajanana and Dhumraketu. Each avatar corresponds to a different yuga, has a different mount and different skin complexion, but all the avatars have a common purpose – to slay demons.
Although Puranic scriptures contain occasional references to avatars of Shiva, the avatar doctrine is neither universally accepted nor commonly adopted in Shaivism. The views on the doctrine of incarnation has been one of the significant doctrinal differences between Vaishnavism and Shaivism, in addition to their differences on the role of householder life versus monastic life for spiritual release. Shaivism is a transcendental theology, where man, with the help of his Guru, is his own savior.
The Linga Purana lists twenty-eight avatars of Shiva. In the Shiva Purana there is a distinctly Saivite version of a traditional avatar myth: Shiva brings forth Virabhadra, one of his terrifying forms, in order to calm Narasimha, an avatar of Vishnu. When that fails, Shiva manifests as the human-lion-bird Sharabha which calms down lion-man Narasimha avatar of Vishnu, and Shiva then gives Vishnu a chakra as gift. A similar story is told in the late medieval era Sharabha Upanishad. However, Vaishnava Dvaita school refutes this Shaivite view of Narasimha.
The monkey-god Hanuman who helped Rama – the Vishnu avatar is considered by some to be the eleventh avatar of Rudra (Shiva). Some regional deities like Khandoba are also believed by some to be avatars of Shiva.
Shesha and his avatars (Balarama and Lakshmana) are occasionally linked to Shiva. Adi Shankara, the formulator of Advaita Vedanta, is also occasionally regarded as an avatar of Shiva.
Avatars are also observed in Shaktism, the sect dedicated to the worship of the Goddess (Devi), but they do not have universal acceptance in the sect. The Devi Bhagavata Purana describes the descent of Devi avatars to punish the wicked and defend the righteous – much as the Bhagavata Purana does with the avatars of Vishnu. Like Vishnu, his consort Lakshmi incarnates as Sita and Radha – the consorts of Rama and Krishna avatars. Nilakantha, an 18th-century commentator on the Devi Bhagavata Purana – which includes the Devi Gita – says that various avatars of the Goddess includes Shakambhari and even the masculine Krishna and Rama – generally thought to be Vishnu's avatars. Lakshmi and Saraswati are main goddesses worshipped as Devi avatars.
Sridevi and Bhudevi are two different forms of the goddess Lakshmi. Dharini, the consort of Parashurama, Sita, the consort of Rama, and Yashodhara, the consort of Siddhartha, along with the consorts of the previous incarnations of Vishnu, are all considered full incarnations of Lakshmi. On the other hand, Radha and the gopis, Rukmini, Satyabhama and the rest of Krishna's wives with the exception of Yamuna, are all considered partial incarnations of Lakshmi.