The different Vedanta schools differ in their perception about Brahman – the ultimate metaphysical reality; Ātman and Jivātman – the individual soul or self, and Prakriti – the empirical ever-changing universe, body and matter.
The Vedanta philosophy is classified mainly as Advaita (non-dualism), Vishishtadvaita (qualified non-dualism), and Dvaita (dualism). Most other Vedantic sub-traditions are subsumed under the term Bhedabheda (difference and non-difference).
We see the rise of Advaitavad, closely identified with Gaudapad (about 500 CE,) and Adi Shankara (800 CE).
Gradually over centuries, Vedanta adopted ideas from other āstika schools like Yoga and Nyaya, and, through this amalgamation of beliefs and faith, it became the most prominent school of Sanatan Dharma.
Significantly, many different forms of Vaishnavism, Shaivism and Shakti also got shaped by the doctrines of different schools of Vedanta during this period. These include Vishisthadvaita (Ramanujacharya), Dvaita (Madhavacharya) and Shuddhadvaita (Vallabhacharya).