In the Hindu philosophical tradition Vedanta means the essence of the Vedas, as described in the Upanishads, the Brahma-Sutras, and the Bhagavad Gita. It includes three main systems of Indian philosophical thought, namely, dualism, as taught by Madhavacharya, qualified non-dualism, as taught by Ramanujacharya, and absolute non-dualism, whose chief proponents are Gaudapada and Sankaracharya. The philosophy of non-dualism, embodying the conclusions of Vedanta, seems to have influenced to a greater or lesser degree all the philosophies and religions of India. It is the unique contribution of the Hindus to the philosophical thinking of the world."
The three basic texts of Vedanta are the Upanishads, the Bhagavad Gita and the Brahma–Sutras. Together they are referred to as the Prasthan-traya or the triple canon of the Vedanta.
In the first chapter which is on Harmony (Samanvaya), Badarayana teaches that the Vedantic texts, taken as a whole, have as their purport Brahman, the non-dual Reality. Badarayana shows that the Vedantic texts harmoniously teach Brahman as the plenary Reality, the world-ground which is of the nature of Existence-Consciousness-Bliss, which is the supreme object of meditation, and which is the final goal to be realised.
In the second chapter which is titled ‘Non-conflict’ (Avirodha), Badarayana discusses the objections that may be raised against the metaphysics of Vedanta. According to Vedanta, Brahman is the substratum, the sole and the whole cause of the universe. Some theistic schools do not subscribe to this view. They hold that God is only the efficient cause who fashions the world out of extraneous matter which is co-eternal with God. Badarayana shows that this view is not sound because God would then become limited and finite. The world (universe) appears from Brahman, stays in it, and gets resolved into it. This does not involve any effort on the part of Brahman. The example of milk turning into curd is useful for realising that there is no need for an external agency for the world to appear. The truth is that the world is not separate from Brahman; it has no independent existence. The effect is non-different from the cause. In other words, the effect is appearance, the cause alone is real. An analogy would be to compare the non-evolution and evolution of the world to the folded and spread out states , respectively, of a piece of cloth. What is the status of the individual soul? Is it the product of Brahman?
In the third chapter of the Brahma-Sutras, Badarayana discusses the means to release-sadhana. If the soul had performed the appropriate meditations, it goes along the path of the gods (Devayana) and reaches Brama-Loka.
The last chapter of the Brahma-Sutras is on ‘The Fruit’ (Phala). Prarabdha is the karma which has begun to fructify and is responsible for the present body. The truth is that for the Jivan-Mukta (liberated ) there is no body at all. The knower of Brahman realises the Absolute, non-different from Brahman. When one has gained release, there is no more involvements in the samsara; no more return to the cycle of birth and death.