Vedanta

Vedanta is the last of the six astika ( believing ) orthodox philosophical systems . Also referred to as the Uttara Mimamsa as against the preceding fifth system of Purva Mimamsa also known just as Mimamsa . Vedanta forms the bedrock of modern Hinduism , and derives considerable authority from the Upanishads .

The name indicates the " end of the Veda " or the culmination of the philosophic thought process and speculation .
The bsaic text is the Brahma Sutra or the Vedanta Sutra of Badarayana , composed between 200 and 400 AD.
It comprises of about 500 verses which are open to intrepretation , therefore requiring commentaries , the most famous ones being that of Sankara , Ramanuja and Madhva .

Advaita

Sankara's school, 8th century AD , is that of pure monoism or Advaita . As per this view only God or Brahman is the ultimate reality and the world is an illusion or Maya .
There is a ordinary truth and a higher truth . From the empirical stand of the ordinary truth , Brahman is Saguna ( with qualities ) and is concieved of as a personal God and creator , such as Vishnu or Siva .
The higher truth is that of transcendental Brahman or an absolute without attributes or qualities, called Nirguna Brahman . Removal of the veil of illusion of Maya , results in one identifying oneself with the Nirguna Brahman and thereby attaining liberation . The aspirant begins with worshipping a personal deity , which diminishes his ego , until the collective identity of all beings in Brahman is experienced . Training under an enlightened Guru is part of the process , who will say to the successful aspirant " Tat Tvam Asi " or " thou art that " , who will meditate on that till he attains liberation .

Ramanuja's school ( 12th and 13th Centuries ) is that of Visishtadvaita or qualified Monoism and Madhva's school (14th Century AD) is of Dvaita or dualism which will be dealt with in due course .