Etymologically the word means that which is unborn or uncreated. Hence it is applied to all the three deities of the Hindu Trinity viz., Brahmā, Viṣṇu and Śiva. It is also applied to the ātman or the self since according to the Hindu scriptures, it is uncreated.
In the Vedic liturgical works, the word denotes the he-goat, considered sacred to Pūṣan (an aspect of Sun) and associated with the sacrificial horse in the Aśvamedha (horse-sacrifice) which is believed to lead the horse to the next world. The skin of a sacrificed goat was used in the Vedic funerary rites for laying the dead body.
In astronomy ‘aja’ indicates the sign Aries.
The Śvetāśvatara Upaniṣad (4.5) compares prakṛti or nature to ajā (she-goat) of three hues (red, white and black, an obvious reference to the three guṇas of sattva, rajas and tamas) and the jīvātman to aja (he-goat) and depicts him as the enjoyer of prakṛti.
Aja is a well-known king of the Ikṣvāku race. He was the son of Raghu, father of Daśaratha and grandfather of Rāma. He was christened ‘Aja’ (= the unborn, i. e., Brahmā) since he was born at brāhmīmuhūrta (the hour preceding sunrise considered as related to Brahmā, the Creator). Indumati, the Vidarbha princess was his queen. She was a celestial maiden born as a human being as a result of a curse. She was delivered from the curse by the sage Nārada. Her untimely death left Aja inconsolable. Kālidāsa devotes three sections (sargas 5, 6 and 7) of his famous poetical treatise Raghu-vaṁśa to the story of Aja and Indumati.
The Ṛgveda (7.18.19) has used the word to indicate the people of the country of Aja who honoured Indra after his victorious war against Bheda, the enemy of Sudāsa.