Dattatreya is the God who is an incarnation of the Divine Trinity Brahma, Vishnu and Siva. The word Datta means "Given", Datta is called so because the divine trinity have "given" themselves in the form of a son to the sage couple Guru Atri and Mata Anusuya. He is the son of Guru Atri, hence the name "Atreya."

In the Nath tradition, Dattatreya is seen as an Avatar or incarnation of the Lord Shiva and as the Adi-Guru (First Teacher) of the Adi-Nath sampradaya of the Nathas. Although Dattatreya was at first a "Lord of Yoga" with Tantric traits, he was adapted and assimilated into the more devotional cults; while still worshiped by millions of Hindus, he is approached more as a benevolent God than as a teacher of the highest essence of Indian thought.

Dattatreya as a historical figure 
Though the Dattatreya of the Natha tradition coexisted and intermingled with the Puranic, Brahmanical tradition of the Datta sampradaya, here we shall focus almost exclusively on the earlier Tantric manifestation of Datta. Shri Gurudev Mahendranath had no doubt that Dattatreya was an historical figure. He stated that Datta was born on Wednesday, the fourteenth day of the full moon in the month of Margasirsa, though he does not mention the year.

Dattatreya left home at an early age to wander naked in search of the Absolute. He seems to have spent most of his life wandering in the area between and including North Mysore, through the Maharashtra, and into Gujarat as far as the Narmada River. He attained realization at a place not far from the town now known as Ganagapur. The original footprints of Datta are believed to be located on the lonely peak at Mount Girnar. The Tripura-rahasya refers to the disciple Parasurama finding Datta meditating on Gandhamadana mountain.

The Tripura-rahasya (The Secret of [the Goddess] Tripura) is believed to be an abbreviated version of the original Datta Samhita or Dakshinamurti Samhita traditionally ascribed to Dattatreya. This more lengthy work was summarized by Dattatreya's disciple Parasurama, whose disciple, Sumedha Haritayana, scribed the text. Thus, this text is sometimes referred to as the Haritayana Samhita.

The Tripura-rahasya is divided into three parts. The first part, the Mahatmya Khanda or section on the goddess is concerned with the origin, mantra and yantra of the Goddess Tripura, also known as Lalita or Lalita Tripurasundari. The Jnana Khanda or section on knowledge elaborates on the themes of consciousness, manifestation, and liberation. The last part, Charya Khanda or section on conduct, has been lost and some believe destroyed.

Another work, the Avadhuta Gita (Song of the Free) is a wonderful, compete compilation of the highest thought given to and recorded by two of Dattatreya's disciples, Swami and Kartika. Swami Vivekananda (1863-1902) held it in high esteem. Originally a work of seven chapters, a spurious and misogynistic eighth chapter may be a later attempt to append sexual morality to the Natha tradition by a conservative ascetic. Some of the ideas in this Gita are however common to both Shaivite and Buddhist Tantras.

The Markandeya Purana reports that Dattatreya, to free himself of all attachments, dove into a lake where he stayed for many years. By doing so, he also hoped to evade an assembly of Munis who remained on the banks of the lake awaiting his return. Datta emerged from the water naked in the company of a beautiful woman. The text relates that he made love with her (maithuna), drank liquor, and enjoyed singing and music. In spite of this, the Munis did not abandon him, and Dattatraya, accompanied by his shakti, continued to engage in these practices and was meditated on by those longing for moksha.

In the Bhagavata Purana Dattatreya enumerates a list of his twenty-four gurus: earth, air, sky / ether, water, fire, sun, moon, python, pigeons, sea, moth, bee, bull elephant, bear, deer, fish, osprey, a child, a maiden, a courtesan, a blacksmith, serpent, spider, and wasp. The image of the Natha ranged from that of a siddha living in the woods with animals, to that of a frightening, even demonic, being.

In The Pathless Path to Immortality, Shri Gurudev Mahendranath writes:

"Shri Dattatreya was a dropout of an earlier age than the period when Veda and Tantra merged to become one simple cult. It was men like Dattatreya who helped to make this possible. Three of his close disciples were kings, one an Asura and the other two both belonging to the warrior caste. Dattatreya himself was regarded as an avatar of Maheshwara (Shiva) but later was claimed by Vaishnavites as the avatar of Vishnu. Not such a sectarian claim as it appears; Hindus regard Shiva and Vishnu as the same or as manifestations of the Absolute taking form."

Indeed, the Dattatreya Upanisad, which opens proclaiming Dattatreya's identity with Vishnu, ends with the mantra Om Namah Shivaya, identifying Datta with Shiva. In the last portion of the third chapter, Mahesvara (Shiva) alone is said to pervade reality and shine in every heart of man. He alone is in front, behind, to the left, to the right, below, above, everywhere the center. Finally, Mahesvara is identified with Dattatreya, depicting the latter as an Avatar of Shiva.

Dattatreya as a devotional deity 
Dattatreya is usually depicted with three heads, symbolising Brahma, Vishnu, and Shiva; past, present, and future; and the three states of consciousness: waking, dreaming, and dreamless sleep. He is portrayed sitting in meditation with his shakti beneath the audumbara (wish-fulfilling) tree. In front of him is a fire pit, and around him are four dogs. These are sometimes said to symbolise the four Vedas.

References 
 Mahendranath, Shri Gurudev. Notes on Pagan India . Retrieved Oct. 14, 2004.
 Mahendranath, Shri Gurudev. The Pathless Path to Immortality . Retrieved Oct. 14, 2004.
 Rigopoulos, Antonio (1998). Dattatreya: The Immortal Guru, Yogin, and Avatara. New York: State University of New York Press. .

Other websites 
Information on Shri Dattatreya - Datta Guru

Hindu gods and goddesses