Advaita means non-dual — a (not) + dvaita (two). Vedanta means the end or culmination of the Vedas — the Upanishads. Advaita Vedanta is the school that reads the Upanishads as teaching, without exception, that reality is non-dual.
The central claim is not that the world does not exist. Not that the individual person is a delusion to be dismissed. The claim is that the deepest nature of the individual self — the bare awareness by which you know you exist — is identical with Brahman, the ground of all existence. The Mahāvākyas express this from four angles: Prajñānam Brahma (consciousness is Brahman), Aham Brahmāsmi (I am Brahman), Tat Tvam Asi (that thou art), Ayam Ātmā Brahma (this self is Brahman).
The school was systematised by Ādi Śaṅkarācārya (c. 788–820 CE), who wrote bhāṣyas (commentaries) on the ten principal Upanishads, the Bhagavad Gītā, and the Brahmasūtras — the three texts that constitute the canonical basis of all Vedanta. Before Śaṅkara, the non-dual tradition was present in the Upanishads themselves and in Gauḍapāda's Māṇḍūkya Kārikā. Śaṅkara gave it a complete philosophical architecture.
All three schools accept the same three canonical texts (Upanishads, Bhagavad Gītā, Brahmasūtras) as their authority. They disagree on what those texts teach about the relationship between the individual self, the world, and Brahman.
Advaita — Non-dual
Ādi Śaṅkarācārya (c. 788–820 CE)
Brahman alone is real. The individual self and Brahman are identical. The world of multiplicity is Brahman appearing through māyā. Liberation is recognition of this identity — possible in this life.
Viśiṣṭādvaita — Qualified non-dual
Rāmānuja (c. 1017–1137 CE)
Brahman is one, but qualified — individual souls and the world are real as the body of Brahman. The soul retains its identity even in liberation, which is eternal proximity to a personal God (Viṣṇu/Nārāyaṇa).
Dvaita — Dual
Madhvācārya (c. 1238–1317 CE)
Brahman (God), individual souls, and the world are eternally and absolutely distinct. Liberation is the soul's eternal beatific enjoyment of God's presence — never merging with God.
Advaita's method is jñāna — knowledge, direct recognition — as the sole means of liberation. But this knowledge is not arrived at by accumulating information. The Advaita tradition describes a threefold preparation for the recognition:
Śravaṇa — hearing the teaching from the teacher. The Mahāvākyas heard from one who knows. This is the first step: exposure to the pointing statement. Manana — reflection. The student tests the teaching against every objection they can raise, resolving doubts through reasoning. Nididhyāsana — deep contemplation, assimilation. The teaching is absorbed until it is no longer a thought about the self but a recognition of the self. The three steps are not a timeline. For some students the recognition occurs during śravaṇa. For others, years of manana and nididhyāsana are required first.
Before these three steps is the preparation described in Vivekacūḍāmaṇi: viveka (discrimination between the real and the unreal), vairāgya (dispassion toward all that is impermanent), śamādi ṣaṭka sampatti (sixfold inner wealth: calm, restraint, withdrawal, endurance, concentration, faith), and mumukṣutva (the burning desire for liberation). These are not prerequisites that must be perfected before inquiry can begin — they are the qualities that deepen through inquiry.