Advaita, given its classical form by Shankara in the eighth century, holds that brahman alone is real, that brahman is without qualities, and that the world and the individual self are superimposed on it by ignorance in the way a rope is taken for a snake. Liberation is therefore the removal of an error rather than the attainment of anything.
Vishishtadvaita, argued by Ramanuja in the eleventh, holds that souls and matter are real and are related to God as a body is related to the self that inhabits it: distinct, dependent, and not a second thing beside him. Dvaita, argued by Madhva in the thirteenth, holds that God and the soul are simply two, and sets out five eternal differences between God, souls and matter that no analysis dissolves.
Others fill the space between. Bhedabheda holds difference and non-difference together, and Vallabha and the Bengali Vaishnava tradition each work variants of that.
The nineteenth century changed the balance. Vivekananda and the reform movements presented Advaita as the philosophical core of Hinduism to audiences in Europe and America, and the version that travelled was adapted for that purpose. Scholars now generally distinguish this Neo-Vedanta from the classical school, and the claim that Advaita is the natural centre of Hindu thought is treated as a modern development that is argued over rather than as an established fact.