The words Brahman and Ātman are extensively used in the Hindu scriptures.
The word ‘Brahman’ has several senses: God the Absolute, the Vedas, a brāhmaṇa, the Brahmā-priest in a Vedic sacrifice as also tapas or austerity. However, it is in the first sense that it is more widely used.
Vidyā means knowledge, wisdom, an art or a science. Hence brahmavidyā refers to that art or science or discipline by practising which, one is able to attain Brahman or God the Absolute.
This brahmavidyā is very ancient and has a hoary tradition. According to the Upaniṣads, Brahmā, the Creator, was himself the first teacher. It has been handed down to us by a galaxy of successive teachers.
One who aspires for brahmavidyā should first cultivate the sādhana-catuṣṭaya or the fourfold spiritual discipline, like viveka (discrimination) and vairāgya (renunciation). (See also SĀDHANACATUṢṬAYA for details.) Tapas (austerity) and devotion to the spiritual preceptor are other aspects of this discipline.
The teacher of brahmavidyā should be a śrotriya (well-versed in the scriptures) and a brahmaniṣṭha (established in Brahman). It is obligatory on his part to impart that knowledge to one qualified for it, if he requests for the same.
The word ‘brahmavidyā’ is sometimes applied to the knowledge of the Vedas and their subsidiary sciences, since Vedas are also known as Brahman.