The Upanishads form one of the three main sources for all schools of Vedanta, together with the Bhagavad Gita and the Brahmasutras. Due to the wide variety of philosophical teachings contained in the Upanishads, various interpretations could be grounded on the Upanishads. The schools of Vedānta seek to answer questions about the relation between atman and Brahman, and the relation between Brahman and the world. The schools of Vedanta are named after the relation they see between atman and Brahman:
- According to Advaita Vedanta, there is no difference.
- According to Vishishtadvaita the jīvātman is a part of Brahman, and hence is similar, but not identical.
- According to Dvaita, all individual souls (jīvātmans) and matter as eternal and mutually separate entities.
Other schools of Vedanta include Nimbarka's Dvaitadvaita, Vallabha's Suddhadvaita and Chaitanya's Acintya Bhedabheda. The philosopher Adi Sankara has provided commentaries on 11 mukhya Upanishads.
Advaita literally means non-duality, and it is a monistic system of thought. It deals with the non-dual nature of Brahman and Atman. Advaita is considered the most influential sub-school of the Vedanta school of Hindu philosophy. Gaudapada was the first person to expound the basic principles of the Advaita philosophy in a commentary on the conflicting statements of the Upanishads. Gaudapada's Advaita ideas were further developed by Shankara. King states that Gaudapada's main work, Māṇḍukya Kārikā, is infused with philosophical terminology of Buddhism, and uses Buddhist arguments and analogies. King also suggests that there are clear differences between Shankara's writings and the Brahmasutra, and many ideas of Shankara are at odds with those in the Upanishads. Radhakrishnan, on the other hand, suggests that Shankara's views of Advaita were straightforward developments of the Upanishads and the Brahmasutra, and many ideas of Shankara derive from the Upanishads.
Shankara in his discussions of the Advaita Vedanta philosophy referred to the early Upanishads to explain the key difference between Hinduism and Buddhism, stating that Hinduism asserts "Atman (Soul, Self) exists", while Buddhism asserts that there is "no Soul, no Self".
The Upanishads contain four sentences, the Mahāvākyas (Great Sayings), which were used by Shankara to establish the identity of Atman and Brahman as scriptural truth:
- "Prajñānam brahma" - "Consciousness is Brahman" (Aitareya Upanishad)
- "Aham brahmāsmi" - "I am Brahman" (Brihadaranyaka Upanishad)
- "Tat tvam asi" - "That Thou art" (Chandogya Upanishad)
- "Ayamātmā brahma" - "This Atman is Brahman" (Mandukya Upanishad)
Although there are a wide variety of philosophical positions propounded in the Upanishads, commentators since Adi Shankara have usually followed him in seeing idealist monism as the dominant force.[note 8]
The Dvaita school was founded by Madhvacharya. Dvaita is regarded as the best philosophic exposition of theism. Madhva, much like Adi Shankara claims for Advaita, states that his theistic Dvaita Vedanta is grounded in the Upanishads.
The third school of Vedanta is the Vishishtadvaita, which was founded by Ramanuja. Ramanuja strenuously refuted Shankara's works. Visistadvaita is a synthetic philosophy bridging the monistic Advaita and theistic Dvaita systems of Vedanta. Ramanuja, just as Madhva claims for Dvaita sub-school, states that Vishishtadvaita is grounded in the Upanishads.