“Advaita” literally means non-dualism. The philosophy of advaita is the oldest among the vedanta schools of Indian philosophy. The  quest is to understand Brahman, the source of everything, and the Atman or the Self, and the relationship between Brahman and Atman. The core teaching in Advaita Vedanta is the identity of the Atman (Jivatma) and Brahman (Paramatma).
For knowledge of Paramatma, we have to rely entirely on Sastra (scriptures). The Rig Veda says Truth (Brahman) is one, though it may be named variously by sages and seers. Though there is diversity in existence, behind it is oneness, which unites all beings through the self. This one consciousness and reality is beyond definition, gender and number. The ultimate reality is beyond space and time. It simply exists without cause or reason. This one reality is not dead or inert, but is the source of knowledge. It encompasses and contains everything.
The real nature of Jivatma, that is, our own real nature, can be known by inward enquiry. The upanishads explore this issue from different angles. According to advaita, the ultimate reality of everything is Brahman, the non-dual pure consciousness and It alone exists. The universe of beings and things is merely an appearance of Brahman in time and space. The individual soul and Brahman are absolutely non-different.
Man suffers from bondage in the course of his life in this world. This is said to be ‘samsara’, which involves being caught in an endless cycle of births and deaths. The quest therefore is to seek a way out of this bondage, to break the cycle of rebirths and attain moksha or liberation. The root cause of all bondage is the ignorance of one’s own true nature. The most important issues in vedanta have to be understood with respect to what constitutes bondage and what constitutes liberation. The advaita school is of the view that jnana (knowledge) of man's true nature is liberation. Bondage arises from ignorance (avidya) of man's true nature. Therefore removal of ignorance roots out this bondage. Liberation is union with Brahman attained through Self-knowledge. This true nature is his innermost essence, the Atman, which is nothing other than Brahman.
Shankaracharya is the most important teacher of the advaita school of Vedanta. His commentaries on the Upanishads, the Bhagavad Gita and the Brahmasutras define the parameters of advaita thought.