There is no single founder of advaita vedanta. Since the philosophy of advaita is rooted in the upanishads, which are part of the eternal vedas, the advaita tradition does not trace itself to a historical personality. However, Adi SankarAcArya is venerated as the most important teacher of advaita vedAnta, as he wrote commentaries to the basic scriptural texts, and placed the living advaita tradition on a firm footing. Before SankarAcArya’s time, the tradition was passed down mainly through oral instruction.
Adi Sankaracharya’s param-guru (guru’s guru) Sri Gaudapada ws also an important acharya in advaita tredition. His celebrated karikas (explonatory extensions) to Madukhya Upanishad are considered valuble in advaitic tradition, in which he explains how this waking world can be seen as unreality just like the dreaming world.
Related: Advaita FAQ