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History
The Upanishads and the Brahma Sutras, being aphoristic in nature, don't deal with rigorous philosophical inquiry. The Upanishads form the basic texts, of which Vedanta gives an interpretation through rigorous philosophical exegesis. Varying interpretations of the Upanishads and their synthesis, the Brahma Sutras, led to the development of different schools of Vedanta over time of which three, four, five or six are prominent.
 * 1) Advaita Vedanta, many scholars of which most prominent are Gaudapada (~500 CE) and Shankara (8th century)
 * 2) Vishishtadvaita, prominent scholars are Nathamuni, Yāmuna and Ramanuja (1017–1137 CE)
 * 3) Dvaita, founded by Madhva (1199–1278 CE)
 * 4) Bhedabheda, as early as the 7th century CE, or even the 4th century. Some scholars consider it apt to consider it as a "tradition" rather than a school of Vedanta.
 * 5) * Upadhika, founded by Bhaskara in the 9th Century
 * 6) * Svabhavikabhedabheda or Dvaitādvaita, founded by Nimbarka in the 13th century
 * 7) * Suddhadvaita, founded by Vallabha (1479–1531 CE)
 * 8) * Achintya Bheda Abheda, founded by Chaitanya Mahaprabhu(1486–1534)

Chronologically, the history of Vedanta is studied as Vedanta prior to the writing of the Brahma Sutras and the schools that developed post the writing of the Brahma Sutras.

Vedanta before the Brahma Sutras
Little is known of schools of Vedanta existing before the composition of the Brahma Sutras(400–450 BC). It is clear that Badarayana, the writer of Brahma Sutras, was not the first person to systematize the teachings of the Upanishads as he quotes six Vedantic teachers before him - Ashmarathya, Badari, Audulomi, Kashakrtsna, Karsnajini and Atreya. References to other early Vedanta teachers - Brahmadatta, Sundara, Pandaya, Tanka and Dravidacharya - are found in secondary literature of later periods. The works of these ancient teachers have not survived, but based on the quotes attributed to them in later literature, postulates that Ashmarathya and Audulomi were Bhedabheda scholars, Kashakrtsna and Brahmadatta Advaita scholars, while Tanka and Dravidacharya were either Advaita or Vishistadvaita scholars.

Brahma Sutras
Badarayana summarized and interpreted teachings of the Upanishads in the Brahma Sutras, also called the Vedanta Sutra. The book is composed of four chapters, each divided into four quarters or sections. The sutras of Badarayana were meant to synthesize the diverse teachings of the Upanishads. However, the cryptic nature of aphorisms of the Brahma Sutras make them difficult to understand without a commentary. This resulted in the formation of numerous Vedanta schools, each interpreting the Upanishads and the Brahma Sutras in its own way in producing its own commentary.

Vedanta between the Brahma Sutras and Adi Shankara
Little is known of the period between the Brahma Sutras(5th Century BC) and Shankara (8th century CE). Shankara mentions 99 different predecessors of his school in his commentaries. A number of important early Vedanta thinkers have been listed in the Siddhitraya by Yamunācārya (c. 1050), the Vedārthasamgraha by Rāmānuja (c. 1050–1157), and the Yatīndramatadīpikā by Śrīnivāsa Dāsa. A noted scholar of this period was Bhartriprapancha, considered an early philosopher of the Bhedabheda tradition. Only two writings of this period have survived: the Vākyapadīya, written by Bhartṛhari (second half 5th century), and the Kārikā written by Gaudapada. opines that at least fourteen prominent thinkers existed between the composition of the Brahma Sutras and Shankara's lifetime.

Gaudapada, Adi Shankara and Advaita Vedanta
Gaudapada (c. 6th century CE), was the teacher of Govindapada, the teacher of Adi Shankara - widely considered the founder of Advaita Vedanta. Gaudapada's treatise - the ', also known as the ' or the  - is the earliest surviving complete text on Advaita Vedanta. To present his ideas in the , Gaudapada relied on the Mandukya, Brihadaranyaka and Chhandogya Upanishads.

In the , Advaita (non-dualism) is established on rational grounds (upapatti) independent of scriptural revelation; its arguments are devoid of all religious, mystical or scholastic elements. Scholars are divided on a possible influence of Buddhism on Gaudapada's philosophy.. The fact that Shankara, in addition to the Brahma Sutras, the principal Upanishads and the Bhagvad Gita, wrote an independent commentary on the  proves its importance in literature.

Adi Shankara (788–820), elaborated on Gaudapada's work and more ancient scholarship to write detailed commentaries on the Prasthanatrayi and the . The Mandukya Upanishad and the  have been described by Shankara as containing "the epitome of the substance of the import of Vedanta". It was Shankara who integrated Gaudapada work with the ancient Brahma Sutras, "and give it a locus classicus", against the realistic strain of the Brahma Sutras. His interpretation, including works ascribed to him, has become the normative interpretation of Advaita Vedanta.

A noted contemporary of Shankara was Mandan Mishra, who regarded Mimamsa and Vedanta as forming a single system and advocated their combination known as Karma-jnana-samuchchaya-vada. Shankara was of the view that Mimamsa & Vedanta are independent of each other and possibly also inconsistent in their central theses. The separation of Vedanta as different from the other orthodox Schools was a contribution of Shankara. Adviata Vedanta rejects ritual in favor of renunciation, which makes Vedanta irreconcilable with Mimamsa.

Ramanuja and Vishishtadvaita Vedanta
Rāmānuja (1017–1137 CE) was the most influential philosopher in the Vishishtadvaita tradition. As the philosophical architect of Vishishtadvaita, he taught qualified non-dualism. Ramanuja's teacher, Yadava Prakasha, followed the Advaita monastic tradition. Tradition has it that Ramanuja disagreed with Yadava and Advaita Vedanta, and instead followed Nathamuni and Yāmuna. Ramanuja reconciled the Prasthanatrayi with the thiesm and philosophy of the Vaishnava Alvars poet-saints. Ramanujan wrote a number of influential texts, such as a bhasya on the Brahma Sutras and the Bhagavad Gita, all in Sanskrit.

Ramanuja presented the epistemic and soteriological importance of bhakti, or the devotion to a personal God (Vishnu in Ramanuja's case) as a means to spiritual liberation. His theories assert that there exists a plurality and distinction between Atman (souls) and Brahman (metaphysical, ultimate reality), while he also affirmed that there is unity of all souls and that the individual soul has the potential to realize identity with the Brahman. Vishishtadvaiata provides the philosophical basis of Sri Vaishnavism.

states that Ramanuja, along with Shankara, is the greatest philosopher of Vedanta. Even as Ramanuja’s contribution to Vedanta thought was highly significant, his influence on the course of Hinduism as a religion was even greater. In integrating Bhakti, the devotional worship into his doctrine of salvation, he aligned the religion of the masses with the pursuits of philosophy while giving bhakti an intellectual basis at the same time. Ever since, bhakti has remained a major force in Hinduism.

Madhva and Dvaita
Dvaita was propounded by Madhva (1238–1317 CE). He presented the opposite interpretation of Shankara in his Dvaita, or dualistic system. In contrast to Shankara's non-dualism and Ramanuja's qualified non-dualism, he championed unqualified dualism. Madhva has left behind him commentaries on the chief Upanishads, the Bhagavad Gita and the Brahma Sutra, besides several other works.

Madhva started his Vedic studies at age seven, joined an Advaita Vedanta monastery in Dwarka (Gujarat), studied under guru Achyutrapreksha, frequently disagreed with him, left the Advaita monastery, and founded Dvaita. Madhva and his followers Jayatirtha and Vyasatirtha, were critical of all competing Hindu philosophies, Jainism and Buddhism, but particularly intense in their criticism of Advaita Vedanta and Adi Shankara.

Dvaita Vedanta is theistic and it identifies Brahman with Narayana, or more specifically Vishnu, in a manner similar to Ramanuja's Vishishtadvaita Vedanta. But it is more explicitly pluralistic. Madhva's emphasis for difference between soul and Brahman was so pronounced that he taught there were differences (1) Between material things; (2) Between material thing and soul; (3) Between material thing and God; (4) Between souls; and (5) Between soul and God. He also advocated difference in degrees in the possession of knowledge and in the enjoyment of bliss even in the case of liberated souls - a doctrine found in no other system of Indian Philosophy.