The first systematic exponent of the Advaita is Gaudapada, who is the Parama-Guru (preceptor's preceptor) of Sri Sankara. Govinda was the disciple of Gaudapada. He became the preceptor of Sankara. Gaudapada has given the central teaching of Advaita Vedanta in his celebrated Mandukya Karikas. But it was Sankara who brought forth the final beautiful form of Advaita philosophy, and gave perfection and finishing touch to it. Carefully go through Sri Sankara's commentaries on the principal Upanishads, the Brahma Sutras and the Bhagavad-Gita. You will clearly understand his Advaita philosophy. The commentary on the Vedanta Sutras by Sankara is known as Sariraka Bhashya.
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.