Anthropomorph."Half fish - half man avatar. He saves the world from a cosmic deluge, with the help of a boat made of the Vedas (knowledge), on which he also rescues Manu (progenitor of man) and all living beings. Demon, Hayagriva steals and tries to destroy the Vedas, but Matsya finds the demon, kills him, and returns the Vedas." https://en.wikipedia.org/wiki/Avatar

"Tortoise avatar. He supports the cosmos, while the gods and demons churn the cosmic ocean with the help of serpent Vasuki to produce the nectar of immortality (just like churning milk to produce butter). The churning produces both the good and the bad, including poison and immortality nectar. Nobody wants the poison, everyone wants the immortality nectar. The demons attempt to steal the nectar, wherein Vishnu appears as enchantress Mohini avatar, for whom they all fall, and give her the nectar." 

Cave 2, Badami Vishnu's boar incarnation rescues the earth goddess, Bhu Devi. Her body bends toward the boar in a graceful arc, as she drapes her right arm over the end of Varaha's muzzle. However, in an evident error of carving, the boar's snout actually stops short of Bhu Devi's arm. Below the main scene is the usual frieze of dancing dwarves.

Iconography and Symbolism of Pañcamukha Nṛsiṁha

Bhutanatha Temples. Badami.

 

Narasiṁha is often visualised as having a human-like torso and lower body, with a lion-like face and claws. This image is widely worshipped in deity form by a significant number of Vaiṣṇava groups. Vishnu assumed this form on top of Himvat mountain (Harivamsa). He is known primarily as the 'Great Protector' who specifically defends and protects his devotees in times of need. Vishnu is believed to have taken the avatar to destroy the demon king Hiranyakashipu.

ETYMOLOGY

The word Narasimha means 'lion-man' which usually means 'half man and half lion'. His other names are:

Agnilochana (अग्निलोचन) - the one who has fiery eyes

Bhairavadambara (भैरवडम्बर) - the one who causes terror by roaring

Karala (कराल) - the one who has a wide mouth and projecting teeth

Hiranyakashipudvamsa (हिरण्यकशिपुध्वंस) - the one who killed Hiranyakashipu

Nakhastra (नखास्त्र) - the one for whom nails are his weapons

Sinhavadana (सिंहवदन) - the whose face is of lion

Mrigendra (मृगेन्द्र) - king of animals or lion

SCRIPTURAL SOURCES

There are references to Narasiṁha in a variety of Purāṇas, with 17 different versions of the main narrative. The Bhagavata Purāṇa (Canto 7), Agni Purāṇa (4.2-3), Brahmāṇḍa Purāṇa(2.5.3-29), Vayu Purāṇa (67.61-66), Harivaṁśa (41 & 3.41-47), Brahma-Purāṇa (213.44-79), Viṣṇudharmottara Purāṇa(1.54), Kūrma Purāṇa (1.15.18-72), Matsya Purāṇa(161-163), Padma Purāṇa(Uttara-khaṇḍa 5.42), Śiva Purāṇa (2.5.43 & 3.10-12), Liṅga Purāṇa (1.95-96), Skanda Purāṇa 7 (2.18.60-130) and Viṣṇu Purāṇa (1.16-20) all contain depictions of the Narasiṁha Avatāra. There is also a short reference in the Mahābhārata (3.272.56-60) and a Gopāla Tapani Upaniṣad (Narasiṁha tapani Upaniṣad), earliest of Vaiṣṇava Upaniṣads named in reference to him.

REFERENCES FROM VEDAS

The Ṛg Veda contains an epithet that has been attributed to Narasiṁha. The half-man, half-lion avatāra is described as:

like some wild beast, dread, prowling, mountain-roaming.

Source: (RV.I 154.2a).

RV 1.154.

1. I WILL declare the mighty deeds of Visnu, of him who measured out the earthly regions,
Who propped the highest place of congregation, thrice setting down his footstep, widely striding.
2 For this his mighty deed is Visnu lauded, like some wild beast, dread, prowling,
mountainroaming-;
He within whose three wideextended- paces all living creatures have their habitation.
3 Let the hymn lift itself as strength to Visnu, the Bull farstriding-, dwelling on the mountains,
Him who alone with triple step hath measured this common dwellingplace-, long, far extended.
4 Him whose three places that are filled with sweetness, imperishable, joy as it may list them,
Who verily alone upholds the threefold, the earth, the heaven, and all living creatures.
5 May I attain to that his wellloved- mansion where men devoted to the Gods are happy.
For there springs, close akin to the WideStrider-, the well of meath in Visnus' highest footstep.
6 Fain would we go unto your dwellingplaces- where there are manyhorned- and nimble oxen,
For mightily, there, shineth down upon us the widelystriding- Bulls' sublimest mansion.

With waters' foam you tore off, Indra, the head of Namuci, subduing all contending hosts.

This short reference is believed to have culminated in the full puranic story of Narasiṁha.

There is an allusion to a Namuci story in RV.VIII 14.13:

RV 8.14.13 With waters' foam thou torest off, Indra, the head of Namuci,

Subduing all contending hosts.

8.014.13 You have struck off, Indra, the head of Namuci with the foam of the waters, when you had subdued all your enemies. [Namuci: legend from s'alya parvan, Maha_bha_rata: Indra after defeating the asuras was captured by Namuci. Namuci however, liberated him on the condition that he would not kill him with any weapon, dry or wet, nor by day or night. In evasion of his oath, Indra at twilight, or in a fog, decapitated Namuci with the foam of water; cf. Taittiri_ya Sam.hita_ 1.8.7]. 

LORD NARASIMHA AND PRAHLADA

RV 1.154

(Griffith translation) RV 1.22. 14 Their water rich with fatness, there in the Gandharvas' steadfast place,
The singers taste through sacred songs.
15 Thornless be thou, O Earth, spread wide before us for a dwellingplace-:
Vouchsafe us shelter broad and sure.
16 The Gods be gracious unto us even from the place whence Visnu strode
Through the seven regions of the earth!
17 Through all this world strode Visnu; thrice his foot he planted, and the whole
Was gathered in his footsteps' dust.
18 Visnu, the Guardian, he whom none deceiveth, made three steps; thenceforth
Establishing his high decrees.
19 Look ye on Visnus' works, whereby the Friend of Indra, closeallied-,
Hath let his holy ways be seen.
20 The princes evermore behold that loftiest place where Visnu is,
Laid as it were an eye in heaven.
21 This, Visnus' station most sublime, the singers, ever vigilant,
Lovers of holy song, light up.