Adi Shankaracharya (c. 788-820 CE) is the philosopher who systematised Advaita Vedanta — consolidating and clarifying teachings found in the Upanishads, Bhagavad Gita and Brahma Sutras into the most rigorous non-dual philosophical system in the world. In a remarkably short life (he died at approximately 32), he wrote extensive commentaries on the principal Upanishads, the Bhagavad Gita and the Brahma Sutras, founded four monastic centres (mathas) across India that continue to transmit the tradition, and debated the leading philosophers of every other school — reportedly defeating them all.
Shankara's central argument: the Upanishads consistently teach that Brahman — the ultimate reality, infinite, consciousness-being-bliss (sat-chit-ananda) — is the only reality. The apparent world of multiplicity is not a second reality alongside Brahman but Brahman appearing as multiplicity through the power of Maya (creative illusion). The individual self (jiva) appears to be separate from Brahman due to ignorance (avidya) — but this apparent separation is itself the illusion. Atman (the individual self) is Brahman. Tat tvam asi — That thou art — is the central Upanishadic declaration.