Amarakaṇṭaka is the holy mountain in the Vindhya-Maikāla range from which the river Narmadā rises. Devas and ṛshis do tapas here. Its holiness cannot be separated from the Narmadā, which the Uttarārdha of the Kūrma Mahā Purāṇa says came from the body of Rudra Himself.

The origin of the Narmadā

The Narmadā is one of the seven holy rivers of Bhāratavarsha. She rises at Amarakaṇṭaka. The Uttarārdha teaches that she did not come only from ordinary earthly sources. She came from the body (śarīra) of Rudra: from the divine sweat and tejas (radiance) that flowed from the body of Parameśvara during His great cosmic tapas. The mountain where this flow became a river is Amarakaṇṭaka.

Those who do tapas, snāna (holy bathing) or japa (repeating a mantra) here receive the greater śakti (power) of both Rudra’s body and the living river that flows from it.

(Kūrma Mahā Purāṇa, Uttarārdha, Chapters 38–40.)

The tapas of devas and ṛshis

Devas, ṛshis and siddhas have done tapas at Amarakaṇṭaka through the ages. Prayers and japa done here bring more fruit.

(Kūrma Mahā Purāṇa, Uttarārdha, Chapters 38–40.)

The course of the Narmadā

From Amarakaṇṭaka the Narmadā flows west for about one hundred yojanas before she reaches the western ocean. Along both banks of this stretch of one hundred yojanas, the Uttarārdha names more than eighty tīrthas (holy bathing places). They include bathing places, Śiva-liṅgas, places of the tapas of ṛshis and places where the divine showed itself. Each carries its own vara (boon). The whole length of the Narmadā is holy from her source at Amarakaṇṭaka.

(Kūrma Mahā Purāṇa, Uttarārdha, Chapters 38–40.)

The Jvāleśvara liṅga: the Padma Purāṇa account

The Svarga Khaṇḍa of the Padma Mahā Purāṇa tells how one of the three Tripura cities of Bāṇa the dānava fell at Amarakaṇṭaka. Bhagavān Śiva made His cosmic chariot (ratha) ready and destroyed Tripura. The three burning cities in the sky then crashed to the earth. One city fell at Śrīśaila, and another fell at Amarakaṇṭaka. The flames from the city that fell here rose up to touch the sky. The devas, asuras and kinnaras cried out in wonder and fear. Bhagavān Śiva then stilled (stambhita) the flames at Amarakaṇṭaka. The spot where the flames were stilled became the place of the Jvāleśvara liṅga. It is a self-appearing liṅga, born from the fire of Tripura.

The Svarga Khaṇḍa says that after the destruction of Tripura, Bhagavān Śiva set up a crore of Rudras at this place. This kshetra, the Jvāleśvara kshetra, gives:

Freedom from rebirth to those who die there.
The reward of ten aśvamedha yajñas for a pilgrimage made during an eclipse (grahaṇa).
The fruit of the puṇḍarīka yajña for those who come during a solar eclipse (sūrya-grahaṇa), when all the tīrthas and devas gather at Amarakaṇṭaka.
A stay in svarga and the fourteen lokas for thirty-one thousand years for visitors, followed by birth as a righteous king.

(Padma Mahā Purāṇa, Svarga Khaṇḍa, Chapter 15.)

The Svarga Khaṇḍa also says that from Amarakaṇṭaka to the meeting of the Narmadā with the sea (Narmadā-sāgara saṃgama) there are ten crore tīrthas.

(Padma Mahā Purāṇa, Svarga Khaṇḍa, Chapter 20.)

The Matsya Purāṇa account

The Narmadā Māhātmya of the Matsya Mahā Purāṇa (Chapter 185) gives the closest account of the tīrthas at Amarakaṇṭaka itself, the source region. Within two krośas of Amarakaṇṭaka there are sixty crore and sixty thousand tīrthas. The foremost of them are:

Rudra-koṭī. A crore of Rudra-liṅgas set up at the source by ṛshis through the ages.
Mahendra-snāna. The bathing place of Indra at the source.

During a solar eclipse (sūrya-grahaṇa) all the tīrthas and all the devas gather at Amarakaṇṭaka. At that moment it is the one holy centre of the whole cosmos. Bathing here during an eclipse gives the merit of ten aśvamedha yajñas. The Matsya Purāṇa also tells that Bāṇāsura’s Tripura fell on the bank of the Narmadā near Amarakaṇṭaka, and that Bhagavān Śiva stilled the flames there and set up the Jvāleśvara liṅga.

(Matsya Mahā Purāṇa, Chapters 185–187.)

Sources

Kūrma Mahā Purāṇa, Uttarārdha, Chapters 38–40
Padma Mahā Purāṇa, Svarga Khaṇḍa, Chapters 15, 20
Matsya Mahā Purāṇa, Chapters 185–187 (Narmadā Māhātmya, Chapter 185)