Shankaracharya - Advaita Vedanta
Advaita Vedanta (IAST Advaita Vedānta; Sanskrit: अद्वैत वेदान्त) espouses non-dualism and monism. Brahman is held to be the sole unchanging metaphysical reality and identical to Atman. The physical world, on the other hand, is always-changing empirical Maya. The absolute and infinite Atman-Brahman is realized by a process of negating everything relative, finite, empirical and changing. The school accepts no duality, no limited individual souls (Atman / Jivatman), and no separate unlimited cosmic soul. All souls and existence across space and time is considered as the same oneness (i.e. monism). Spiritual liberation in Advaita is the full comprehension and realization of oneness, that one's unchanging Atman (soul) is the same as the Atman in everyone else, as well as being identical to the nirguna Brahman.
Ramanujacharya - Vishishtadvaita
Vishishtadvaita asserts that Jivatman (human souls) and Brahman (as Vishnu) are different, a difference that is never transcended. With this qualification, Ramanuja also affirmed monism by saying that there is unity of all souls and that the individual soul has the potential to realize identity with the Brahman. Vishishtadvaita, like Advaita, is a non-dualistic school of Vedanta in a qualified way, and both begin by assuming that all souls can hope for and achieve the state of blissful liberation. On the relation between the Brahman and the world of matter (Prakriti), Vishishtadvaita states both are two different absolutes, both metaphysically true and real, neither is false or illusive, and that saguna Brahman with attributes is also real. Ramanuja states that God, like man, has both soul and body, and the world of matter is the glory of God's body. The path to Brahman (Vishnu), according to Ramanuja, is devotion to godliness and constant remembrance of the beauty and love of the personal god (bhakti of saguna Brahman).
Vallabhacharya - Shuddhādvaita
Shuddhadvaita (pure non-dualism) states that the entire universe is real and is subtly Brahman only in the form of Krishna. He agreed with Advaita Vedanta's ontology, but emphasized that prakriti (empirical world, body) is not separate from the Brahman, but just another manifestation of the latter. Everything, everyone, everywhere—soul and body, living and non-living, jiva and matter—is the eternal Krishna. The way to Krishna, in this school, is bhakti. Vallabha opposed renunciation of monistic sannyasa as ineffective and advocates the path of devotion (bhakti) rather than knowledge (jnana). The goal of bhakti is to turn away from ego, self-centered-ness and deception, and to turn towards the eternal Krishna in everything continually offering freedom from samsara.