Advaita Vedanta is non-dualism or monism, the doctrine that declares that there is but one reality, that the individual Self and the Brahman are one.
The three schools of Vedanta philosophy differ on the way in which they define the relation between the Absolute, called Brahman, and the world. The world here includes both the material world, the non-living objects, and the living, our souls. The three schools are:
Dvaita: the school of Dualism. In this, the Absolute and the world are two completely separate and different entities, and Brahman has created and supports the world. Here humans are seen in a subservient role to the Absolute.
Vishista Advaita: this is the path of Qualified Monism. Here also, the Absolute and the world are two separate entities but God or Brahman has created us out of His own substance, and we are a part of God. The analogies given are the fire and sparks, the sea and wave, clay and pot,etc. In this, we are nearer to the Brahman because we enjoy a relation of part and whole, and thus we can seek Brahman within our own hearts.
Advaita: Advaita is the path of Monism. Dvaita means dualism and hence Advaita means Non-dual. Here, the reality of the world is denied and the Absolute is said to be the only reality. The world is said to have only relative reality, and therefore its reality is ambiguous, and it is only Brahman which is the root of the world which has reality.
The chief exponent of Kevala Advaita or Advaita is Shankaracharya. He lived around the eight century. He had a large number of achievements to his credit. He wrote commentaries on the ten principal Upanishads, The Bhagavat Geeta and the Brahma Sutras. He traveled around the country and established Advaita, and was one of the chief factors that led to the eventual downfall of Buddhism in India. Other important teachers of Advaita are Vacaspati Misra and Prakasatman, and also Mandana, Padmapada and Suresvara.
Advaita Vedanta does not deny the reality of the world completely. It does not say that this world does not exist at all, it only denies that the world has absolute reality. The things of the world do exist, but they exist only as half real things without any absolute reality.