There is only one Reality, Brahman. The world is not the ultimate reality. World is the relative reality. It appears and disappears. The individual self, Jivatma is identical with the Supreme reality, Paramatma (or Brahman). Since Brahman alone exists, all the diversities are real, but not the reality. Brahman is impersonal, non-dual, transcending all attributes. Brahman is Nirguna and it always exists.
The supreme consciousness, Brahman has unimaginable and infinite power and it is non-dual. There cannot be a second entity. Advaita philosophy has dealt considerably with Maya. Maya is the power of Brahman. It causes the world to be real, at the same time it is distinct from Brahman. Brahman projects itself into different forms and names by its eternal power Maya. Sankaracharya explains the Advaita philosophy with mainly two metaphors, the mud and the mud pot, gold and gold ornaments. The mud, when processed takes the form of the pot. When we break the pot, it loses its name and form and it again changes in to mud. Similarly, we make ornaments with pure gold. When we melt the ornaments, it loses its name and form and it again becomes gold. Likewise, Brahman appears in different names and forms. When it loses its different names and forms, it is Brahman alone. The waves of the ocean are nothing but ocean in the form of the waves. Likewise, the different forms of the universe are nothing but Brahman in different forms. The world is real (subject to change) and not the reality. Brahman alone exists, and the rest is illusion.
The essence of Sankara’s philosophy is “Brahma Satya Jagat Mithya, Jivo Brahmaiva Na Aparah”. That is, “Brahman (the absolute) alone is real; this world is unreal, and the Jiva or the individual soul is non-different from Brahman”.
The Jiva or the individual soul identifies itself with the body-mind complex due to Avidya (ignorance). Its individuality lasts only as long as it identifies itself with its limiting adjuncts. The moment the Jiva understands its infinite power by Jnana (knowledge), it loses its individuality and realizes its Satchitananda nature (infinite nature). Then the Jiva attains liberation. Sankaracharya wrote commentaries for Prasthana Trayi based on the Advaita philosophy. Many people could not understand his profound philosophy. They refuted his philosophy. After Sankaracharya, the theologians of various sects of Hinduism utilised Vedanta to a greater or lesser degree to form the basis of their doctrines.
In the 7th century AD, the Vaishnava movement became prominent in South India. At the end of the 9th century AD, Nathamuni, the head priest of the Srirangam temple (Tamil Nadu) guided this movement seriously. It is said that, Nathamuni received the Tamil devotional hymns written by the twelve Alwars, called the Nalayira Divya Prabandham (4000 poetry) from Nammalwar , the foremost of the twelve Alwars in yogic insight. He classified them, set the hymns to music and spread them everywhere. After his period, his successor Yamunacharya laid the fundamentals of Vishishtadvaita philosophy. His successor is Ramanujacharya (1017-1137) AD. Ramanujacharya developed and spread the Vishishtadvaita philosophy throughout India. Ramanuja’s path is mainly based on devotion. He strongly refuted the Kevala Advaita philosophy. Ramanujacharya was the foremost thinkers to identify the personal God with Brahman or Absolute reality.