The doctrine of advaita vedanta as expounded by Sankara can be summed up in half a verse: “Brahma Satyam Jagan Mithya Jivo Brahmaiva Na Aparah" — Brahman (the Absolute) is alone real; this world is unreal; and the Jiva or the individual soul is non-different from Brahman. This is the quintessence of his philosophy.
According to Sri Sankara, whatever is, is Brahman. Brahman Itself is absolutely homogeneous. All difference and plurality are illusory.
The Atman is self-evident (Svatah-siddha). It is not established by extraneous proofs. It is not possible to deny the Atman, because It is the very essence of the one who denies It. The Atman is the basis of all kinds of knowledge, presuppositions and proofs. Self is within, Self is without; Self is before, Self is behind; Self is on the right, Self is on the left; Self is above and Self is below.
The Advaita philosophy of Sri Sankaracharya is lofty, sublime and unique. It is a system of bold philosophy and logical subtlety. It is highly interesting, inspiring and elevating. No other philosophy can stand before it in boldness, depth and subtle thinking. Sankara’s philosophy is complete and perfect.