Vamana

Vamana, also known as Trivikrama, Urukrama, Upendra, Dadhivamana, Ulagalanthan and Balibandhana, is an avatar of the Hindu deity Vishnu. He is the fifth avatar of Vishnu and the first Dashavatara in the Treta Yuga, after Narasimha.
First mentioned in the Vedas, Vamana is most commonly associated in the Hindu epics and Puranas with the story of taking back the three worlds from the daitya-king Mahabali by taking three steps to restore the cosmic order and push Mahabali into the netherworld. He is the youngest among the adityas, the sons of Aditi and the sage Kashyapa.

Nomenclature and etymology

'Vāmana' means 'dwarf', 'small' or 'small or short in stature'. It also means 'dwarfish bull', which is notable as Vishnu is directly associated with dwarfish animals in the Vedas. Stated in Puranic literature to be born of the great sage Kashyapa and his wife Aditi, other names or epithets referring to Vamana include:

Name	Sanskrit	Meaning / Description
'Balibandhana' or 'Balibandhanakrt'	बलिबन्धन	'binder or killer of Bali'; stated in the Garuda Purana to mean 'who fettered the demon Bali'.
'Dadhi-vamana'	दधिवामन	'bestowing', 'giving', 'curd' / 'curdled milk', and 'resin of Shala tree'.
'Trivikrama'	त्रिविक्रम	'three steps' or 'three strides'. This epithet refers to the three steps or strides of Vishnu in the Rigveda.
'Urukrama'	उरुक्रम	'far stepping' or 'wide stride', presumably in relation to covering all existence with the second step.
'Upendra'	उपेन्द्र	'younger brother of Indra' or simply 'a son'. This epithet refers to the birth of the Dwarf Avatar as one of the 12 adityas - sons - of Aditi and the sage Kashyapa.
'Vāmanadeva'	वामनदेव	'dwarf-god'.

Legend

After Indra is defeated by the daitya called Bali, the king of the asuras, the great-great grandson of Kashyapa and Diti, the devas ultimately seek refuge in Vishnu, who agrees to restore Indra to power. To do so, Vishnu incarnates as Vamana
Mahabali decided to perform a grand Ashwamedha Yagna at a place called Bhrigukachaka on the northern bank of the Narmada River.
Vamana come there, who requests only three feet of land. Bali agrees, despite being warned about Vamana's true nature as Vishnu.
Vamana grew as Trivikrama. With one foot, he measured the entire Earth and the nether worlds, and with the other foot, he measured the sky and the upper worlds.
He looked at King Bali and asked where the third step should land.
Determined to keep his word, King Bali told Vamana to place the third step on his head.Upon hearing this, Lord Vishnu appeared in his true form and blessed King Bali and allowed him to rule the underworld.
So Bali went to Pathala
the netherworld. Due to the Vamana incarnation of Lord Vishnu, Indra and other gods retained Amaravati.

Symbolism

A. A. Macdonell states that the 'reason why Visnu took his three steps is a secondary trait. He thrice traversed the earthly spaces for man in distress ; he traversed the earth to bestow it on man for a dwelling ; he traversed the earthly spaces for wide-stepping existence ; with Indra he took vast strides and stretched out the worlds for our existence. This feature in the may ultimately be traced to the myth of Vishnu's dwarf incarnation which appears in the epics and Puranas. The intermediate stage is found in the Brahmanas, where Vishnu takes the form of a dwarf, to reclaim the earth for the devas by means of sacrifice.The three points in sun's course: Roy states that 'Vishnu's three strides alluded to in the Rigveda have been variously interpreted as symbolizing the three different positions of the sun at its rising, peak and setting.
The three worlds and the three planes: J. Muir mentions Sayanas take on the three steps of Vishnu found the White Yajurveda. 'Vishnu, becoming incarnate as Trivikrama, strode over the whole universe. The same idea is expressed by the Rishis, "In three places he planted his step, as Agni, Vayu, and Surya each after the other". Agni is found on the ground, Vayu prevades the atmosphere and Surya high in the dome of sky, thus the three steps symbolise the three planes, the ground below, air in between, and the sky above.
Three states of sleep and wakefulness: S. Chanda states the three strides symbolize the three states of existence – Jagrat, Swapna and sushupti. The final step of Vamana is on the head of Bali which symbolizes Liberation and the transcendence of these states.

Nirukta

Written by the grammarian Yaska, Nirukta is one of the six Vedangas or 'limbs of the Vedas', concerned with correct etymology and interpretation of the Vedas. The entry for Vishnu states :
This account essentially states that the three footsteps may symbolise the positions of the sun or physical existence conceptualised as 'three worlds'. In regard to the references to Sakapuni and Aurnavabha, K. S. Murty states that 'Yaska was not the first to interpret Vedic words as he did. He referred to a Nighantu with Samamnaya which he cited and explained. He had predecessors like Sakapuru, Audumbarayana, Aupamanyava and others'.

Vedas

Rigveda

Samhita

Roy states that the Rigvedic passages referring to Vishnu's three strides are obviously the nucleus, out of which the legend of the Dwarf was created. But the Rigveda, however, does not describe Vishnu as dwarf or Vamana'. W. J. Wilkins agrees, stating that in regard to the Vishnu strides of the Rigveda, 'in these verses there is probably the germ of the Dwarf Incarnation'.
In regard to the above-quoted verses, it is commonly accepted that there are Seven Continents or 'regions of the earth'. A. Glucklich adds that 'In the Matsya Purana, for instance, there is a seven-part map of the world... one centre, where an immense mountain – Mount Meru – stands... The continents encircle the mountain in seven concentric circles... It seems clear that the Himalayas were the approximate location of Mt. Meru'.
In regard to the three steps of Vishnu, Glucklich points out that in some legends of Vamana and the Asura-King Bali, that 'the first covered the entire earth, the second covered the atmosphere, and the third measured heaven in its entirety'. M. Haug, in his translation of the Aitareya Brahmana of the Rigveda, clarifies that the 'three worlds' often means the Ground, the Air, and the Sky. Three steps thus encompasses all of physical existence. D. Goodall also relates more a mystical interpretation of what 'three worlds' symbolises, as provided by the Brihadaranyaka Upanishad, including Mind, Speech, and Breath.
Notably, Muir also states that although 'Adabhya' can be translated as 'who cannot be deceived', it can also be translated as 'the unconquerable preserver', and notes that the 'idea of Vishnu being preeminently the preserver of the universe, which became current in later times , may possibly have been derived from this verse'.

Aitareya Brahmana

The concept of Vishnu obtaining the three worlds for the Devas from the Asuras in three steps is clearly explained in the Aitareya Brahmana. The Rigveda Samhita verse referred to regarding Indra and Vishnu battling the Asuras states 'Ye Twain have conquered, ne’er have ye been conquered: never hath either of the Twain been vanquished. Ye, Indra-Vishnu, when ye fought the battle, produced this infinite with three divisions'.
The Maruts, referred to as 'the sons of Rudra' are frequently mentioned throughout the Rigveda, including in relation to the above quotation, producing rain. Indra is the god of rain and as stated in the Aitareya Brahmana, 'rain gives food'. This is elaborated upon in the Aitareya Aranyaka which states "the seed of the devas is rain. The seed of rain is herbs. The seed of herbs is food". Additionally, in the Bhagavad Gita, Krishna states 'All living bodies subsist on food grains, which are produced from rains. Rains are produced by performance of yajna'.

Sama Veda

Samhita

The translator, R.T.H. Griffith, states in his introduction to the Sama Veda that it 'is made up of hymns, portions of hymns, and detached verses, taken mainly from the Rigveda'. The above-quoted Sama Veda hymn, for example, is taken directly from Rigveda hymn 1.22.

Pancavimsa Brahmana

The terms 'stoma' and 'saman' from the above-quoted Pancavimsa Brahmana refer to mantras and hymns, such from the Sama Veda.
The Jaiminīya Brahmana has a similar verse which omits Vishnu's strides but explains the Varavantiya saman as 'He who desired cattle should apply the Varavantiya Saman. Prajapati created the animals. Having been created they ran away from him. By means of the Varavantiya Saman he held them back. Because he held them back therefore the Varavantiya is called the Varavantiya. The application of the Varavantiya as the agnistoma Saman is made in order that the animals remain present and do not run away'.
In the Taittiriya Samhita 5.5.8 Varavantiya is also explained as 'Prajapati created Agni; he , created, went away from him; him he checked by the Varavantiya, and that is why the Varavantiya has its name. By the Cyaita he congealed him, and that is why the Cyaita has its name. In that he reverences, with the Varavantiya, he restrains him, and by the Cyaita he congeals him'.
The strides of Vishnu are thus referred to in regard to restraining animals from running away from sacrifices. This idea of being restrained by Vishnu strides may be linked to Bali often being restrained or bound in the legend of Vamana.