In India swans appear both as the hamsa and as apsaras.
Brahma’s consort Saraswati, goddess of wisdom, learning, and music, is also depicted riding on a swan (hamsa), as is Varuna, god of the sky and rain.
In Hindu lore, the hamsa (a pair of divine birds) can be either swans or geese. The two are interchangeable. The word hamsa is a cognate of the Latin anser (goose).
The hamsa lives on Lake Manasarovar in Tibet, from which it migrates to India in the winter. It is extolled as the king of birds, and said to eat pearls and be able to separate milk from water when the two are mixed. It trancends creation, because it can fly in the sky, swim in the water, and walk on the earth. The hamsa represents perfect union, balance and life (breath and spirit).
In Vedic times, the hamsa was connected with Surya, the sun god. Iit signified strength and virility. In the Upanishads, the hamsa acquired more attributes, symbolizing purity, detachment, divine knowledge, prana (cosmic breath) and spiritual accomplishment.
The hamsa laid a golden egg on the waters. (This is the same role taken by the goose in ancient Egypt.) From that egg sprang the god Brahma, the Creator. In the Upanishads, the hamsa is said to possess the sacred knowledge of Brahma. Therefore, it symbolizes the elevation of the unformed toward the Heaven of Knowledge. Brahma is often depicted riding on the hamsa.
The hamsa is also used as a symbol of Narayana, an aspect of Vishnu, the Preserver. In this context, the hamsa is a personification of the soul in the universe. The flight of the hamsa symbolizes the escape from the cycle of samsara, rebirth.
The hamsa is also identified with Shiva, the Destroyer. Cambodian literature identifies Shiva both with Kalahamsa (who haunts the yogis’ lake of the heart) and with the hamsa (which dwells in the binou). Here, the hamsa symbolizes the atman, the universal self.
A constant repetition of the word “hamso” changes it to “soaham”, which means “That I am”. Therefore, the hamsa is identified with Brahman, the supreme spirit. When inverted, ham-sa reads sa-ham, which in Sanskrit means “the oneness of the human and divine”. During pranayama, a form of breath control in yoga, inhalation is said to sound like ham, and exhalation is said to sound like sa. So, hamsa symbolizes the prana, the breath of life.
In the philosophy of Advaita Vedanta, an Adavaitan lives in the world of maya, unsoiled by its illusion, just as a swan lives on water without getting its feathers wet.
The hamsa is carved on temples to symbolize the perfect union to which celestial beings aspire. Reliquaries in the shape of hamsa were used to hold the ashes of deceased persons.
The title paramhamsa (supreme hamsa) is prefixed to the names of saints and holy people, symbolizing that the person has reached a high level of spirituality and emancipation.
The apsaras of Hindu and Buddhist lore are female spirits, often represented in the form of swans. The ancient Indians pictured the sky as a heavenly lake, with the clouds as female spirits in the form of swans bathing in that lake. They are said to be able to change their shapes at will. [Sabine Baring-Gould, Curious Myths of the Middle Ages (1866-1868]The apsaras are the handmaidens of Indra, the Lord of Heaven. They dance before his throne. As patrons of the performing arts, the apsaras are analogs of the Muses of Greek mythology. Some of them are wives of thegandharvas, the nature spirits who are servants of Indra. One of their duties is to guide heroes who fall in battle to paradise, where they become their wives, a role similar to the Muslim houris and the Norse valkyries.Apsaras may be either daivika (divine) or laukika (worldly). The worldly asparas often lure men to their deaths. They sometimes descend to earth, becoming the wives of mortal men. Eventually, however, they return to their celestial home. [Baring-Gould.]Nicayadatta, a mortal, caught one of these celestial maidens, then lost her. Deeply in love, he pursued her to the golden city that was her true home.
Sridatta, another mortal, saw an apsara bathing in the Ganges. He plunged in after her, and found himself in a wondrous land beneath the water, in the company of his beloved.
The Siddhi-Kur tells the story of a woman who had three daughters. The girls took turns keeping the cattle. The eldest was taking her turn when she lost an ox. She went in search of it. She came to a cave, which she entered, finding a beautiful lake surrounded by flowers, on which was swimming a silver swan. She asked for her ox. The swan told her she could have it back if she would become his wife. She refused, and returned to her mother. The next day the second sister also lost an ox. She traced it to the cave, asked the swan to return it, refused to become his wife, and also returned to her mother. On the third day, the youngest daughter also lost an ox. Tracing it to the cave, she agreed to become the swan’s wife, and got back all three oxen. [Baring-Gould.]