One of the major theological cum philosophical schools of the Vedānta darśana, now closely associated with the teachings of Śaṅkara (Śaṅkarācārya). The earliest identifiable Advaita text, the Gauḍapādīya Kārikā, was said to have been composed by Śaṅkara's paramaguru (his teacher's teacher), Gauḍapāda. The Kārikā propounds the non-dual (advaita) nature of ultimate reality (brahman (neut.), and the complete identity of brahman and ātman. It regards the world of apparent change and multiplicity as ultimately an illusion (māyā), and teaches that nothing has ever really come into existence (ajātivāda doctrine). Śaṅkara wrote a commentary on the Kārikā, and it was clearly a major influence on the development of his own thought, at the core of which is the perception that brahman alone is real, in the sense of being the one, indivisible existent. Much of his exegesis is therefore taken up with explaining the nature of the apparent (because ultimately unreal) relationship between brahman and the individual (ātman), and, by extension, the nature of conventional experience. At the core of this is superimposition (adhyāsa), the mistaken belief that an object has certain attributes which in reality it does not have, classically illustrated by the man who, in the dark, mistakes a coiled rope for a snake. By analogy, this explains the way in which, according to Śaṅkara, reality or brahman (which is actually beyond nāmarūpa—names and forms—and devoid of all distinctions) comes to be experienced, under the superimposition of names and forms, as the world of appearances. This persistent mistaking of appearance for reality is the source of ignorance (avidyā); conversely, liberating knowledge (vidyā) is the ability to distinguish between what is superimposed on the self and its true nature, which is brahman. With this discrimination (viveka), it is not just avidyā that is dispelled, but also māyā, the cosmic power of ‘illusion’ or artifice, which is coeval with ignorance, and its ultimate cause. For Śaṅkara, the logical problems caused by attributing reality or unreality to avidyā itself are irrelevant to the soteriological imperative of realizing its ultimate disconnection from brahman or the self. (Later Advaitins, however, continued to wrestle with the conundrum of avidyā's ontological status.) Discursive knowledge of the world of appearances, of names and forms, is characterized by Śaṅkara as vyavahāra (‘conventional’ or ‘relative’), as opposed to the paramārtha (‘supreme’ or ‘absolute’) knowledge which is the direct realization of the non-dual brahman/ātman. Similarly, he distinguishes between saguṇa brahman (brahman as experienced through conventional knowledge, i.e. as Ῑśvara, a personal deity and object of devotion) and nirguṇa brahman (brahman experienced as the non-dual reality, transcending all qualities and categories). (Although, following the Upaniṣads, the latter state is characterized by later Advaitins as the reality/state of being which is pure consciousness and bliss (saccidānanda).)
According to Śaṅkara, liberating knowledge of brahman can only come from Vedic revelation (essentially the Upaniṣads); it is therefore only accessible to those of the twice-born varṇa who have, at the very least, received upanayana and undertaken Vedic studentship (brahmacarya). He differs from the Pūrva Mīmāṃsakas in so far as that, while he regards ritual (karma) as necessary in order to remove the impurities which obstruct knowledge, he considers it to be incapable, in itself, of bringing the highest goal of liberation or immortality. That is to be achieved through reflection and meditation on the true nature of the self, knowledge of which can only be gained, in the first instance, through hearing the seemingly external voice of Vedic revelation (i.e. through the teachings of the jñānakāṇḍa—especially, according to the tradition, the mahāvākya). The ritual life should therefore culminate in renunciation, something which, according to Śaṅkara, can be done from any āśrama.