The teachings of 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.
The Advaita taught by Sri Sankara is a rigorous, absolute one. According to Sri Sankara, whatever is, is Brahman. Brahman Itself is absolutely homogeneous. All difference and plurality are illusory.