Brahmavidya is an ancient philosophy which could be considered the core of Hindu philosophy. It is the teachings at the heart of the Upanishads. A well-known example of this is the Yoga Philosophy. In ancient Sanskrit philosophical literature the term Brahma is used to denote the Supreme Being, also called Atma. Hence Brahmavidya is a teaching, which leads to knowledge of Brahma.
It emphasizes the role of meditation in realizing the spiritual nature of a person and uses exercises involving breathing to support and nurture nature ability. The subconscious mind is assigned the central role in bringing about physiological and spiritual transformation. Exercises related to the subconscious mind are therefore also crucial to this system.
The system of Vedanta, like Yoga, is based on Brahma-Vidya; Vedanta has 3 branches, Advaita, Vishithadvaita, and Dvaita.
Brahma-Vidya is often credited to the Rshi Vasishtha, who is also an author of the Vedas; this is why Brahma-Vidya can also be considered the core phillsophy of the Vedas, as well as the Upanishads which are based off of them.