Tryambakeśvara is one of the twelve Jyotirliṅgas of Bhagavān Śiva. It stands near the Brahmagiri hill in present-day Maharashtra, at the source of the sacred Godāvarī river. Bhagavān Śiva appeared here as Tryambaka, the three-eyed lord, in answer to the tapas (austerity) of Gautama Maharshi. The Gaṅgā came down here and became the Godāvarī.

The Jyotirliṅga of Tryambaka marks the birth of a great sacred river and the lasting home of Bhagavān Śiva.

Origin: Gautama’s tapas and the death of a cow

The Nārada Mahā Purāṇa (Uttarardha, Chapter 73) ties Tryambakeśvara to the narrative of Gautama Maharshi. By the touch of a blade of darbha grass, Gautama caused the death of a cow by accident. The devas counted this as go-hatyā (the killing of a cow). Though he was blameless, Gautama was filled with grief and distress.

To make himself pure, Gautama performed hard tapas. He called on Bhagavān Śiva to come to his āśrama (hermitage) on the Brahmagiri hill and give him the waters of Gaṅgā.

Bhagavān Śiva was pleased with Gautama’s tapas and appeared at this spot. He brought Gaṅgā down from svarga (heaven). This was not the Gaṅgā that flows through the northern plains. It was a new descent of the divine waters. Where the waters fell and flowed, the sacred river Godāvarī was born. The Godāvarī is another form of Gaṅgā, the southern Gaṅgā (Dakshiṇa Gaṅgā), born of the grace of Bhagavān Śiva through the tapas of Gautama.

Bhagavān Śiva as Tryambaka

Bhagavān Śiva made his home at this spot for ever as Tryambakeśvara, “the lord with three eyes”. The Jyotirliṅga appeared here of its own divine will. The name Tryambaka points to his third eye, the eye of knowledge beyond this world. The Jyotirliṅga is the point where the Godāvarī begins and the lasting seat of his grace for Gautama and for all pilgrims. (Nārada Mahā Purāṇa, Uttarardha, Chapter 73)

Merit of darśana at Tryambakeśvara

Those who visit Tryambakeśvara and bathe in the Godāvarī at its source receive these fruits:

Full cleansing from go-hatyā and other mahāpātakas (great sins)
The fruit of performing a Rājasūya yajña
Śiva-loka after death
Freedom from the fear of punarbhava (rebirth)

The Uttarardha says that a person who bathes where the Godāvarī begins and has darśana (sacred sight) of Tryambakeśvara on the same day receives the combined fruit of bathing in the Gaṅgā and in all twelve Jyotirliṅga kshetras. (Nārada Mahā Purāṇa, Uttarardha, Chapter 73)

The Brahma Mahā Purāṇa account

The Gautamī Māhātmya of the Brahma Mahā Purāṇa tells of the Tryambaka site in full, over several chapters (5 to 9). The cow’s death was brought about by scheming ṛshis, and Vināyaka had a plan to bring Gaṅgā to earth. Gautama then obtained Gaṅgā from the matted locks of Bhagavān Śiva at Kailāsa and led the river back to Brahmagiri.

On the summit of Brahmagiri he set down his matted hair. Gaṅgā came down there as the Gautamī and divided into fifteen channels, running to svarga, the earth and the nether worlds. Bhagavān Śiva gave the river six sacred names and declared her the holiest of all rivers. He said it three times.

The Gautamī Māhātmya names the place where the Tryambakeśvara liṅga first appeared as the spot where Bhagavān Śiva showed himself to Gautama. The Varāha Purāṇa account says this was after a hundred years of tapas. The Brahma Purāṇa account says it was after the singing of the Ashṭamūrti stotra (hymn of praise). The Brahma Purāṇa also says that Brahmā himself calls Tryambakeśvara the first among all the holy centres told of in the Gautamī Māhātmya. This is the tīrtha where the three-eyed lord showed himself. The Varāha tīrtha lies next to it, and the two together are the opening holy places of the whole Gautamī Māhātmya.

Sources

Nārada Mahā Purāṇa, Uttarardha, Chapter 73
Brahma Mahā Purāṇa, Gautamī Māhātmya, Chapters 5–9
Varāha Purāṇa (named for the account of a hundred years of tapas; no chapter given)