Advaita Vedanta is probably the best known of all Vedanta schools of Hinduism, the others being Dvaita and Vishishtadvaita. Nondual Vedanta is considered the pearl of Indian philosophy and it has influenced virtually all schools of Indian thought.
The key texts from which all Vedanta texts draw are the Upanishads (especially 12 or 13 in particular), which are commentaries on the Vedas, and the Brahma Sutras (also known as Vedanta Sutras), which is in turn constitute a work discussing the essence of the Upanishads. The nondual message of the Upanishads, of the Bhagavad Gita, and of the Brahma Sutra is that only the one Absolute, the Undivided Self is real, It being the only Truth to be seen, surrendered to and ultimately realized.
The pillar of Advaita Vedanta was Adi Shankara (788-820 AD), who consolidated the principles of Advaita. Continuing the line of thought of some of the Upanishadic teachers, and also that of his own teacher Gaudapada, Shankara expounded the doctrine of Advaita – a nondualistic reality.
The supreme truth of Advaita is the nondual reality of Brahman, in which atman (the individual soul) and brahman (the ultimate reality) are identified absolutely. It was Adi (meaning “first” in Sanskrit) Shankara who gave Advaita its name and actively tried to spread its ideas.
He systematized his conceptions of nondualism and its practice into coherent works such as the Viveka-Chudamani (Crest-Jewel of Discrimination) and Brahma Bhashyas, which are commentaries on the Brahma Sutras. Adi Shankara’s contributions to Advaita thought and Hinduism in general are crucial. He revived monism in India and brought a profound understanding of existence.
He considered that the ultimate truth was Brahman, the one divine ground that is beyond time, space, and causation. He did not mean to negate the phenomenal universe, but rather the identification of our true nature with the ephemeral structures, such as body, psyche, and mind. Indeed, while Brahman is the efficient and material cause for the cosmos, Brahman itself is not limited by its self-projection and indeed transcends all binary opposites/dualities, especially such individuated aspects as form and being, since it is incomprehensible by the human mind.
The limitless Self cannot be comprehended by mind. Transcending the mind is the path of recognizing our ultimate essence, atman.
Later Vedantins debated whether the reality of Brahman was saguna (with attributes) or nirguna (without attributes). The spreading of devotional attitudes had its roots in the belief in the concept of Saguna Brahman. However, it is important to mention that Advaita Vedanta did not deny Saguna Brahman. Shankara counseled worship of God in different forms, and has composed numerous works deploring the uselessness of intellect and calling for the true intuition of the heart to be found in love of the Lord.
Advaita Vedanta is commonly misperceived as an intellectual philosophy, whereas it is quite practical, seeking to awaken discrimination (viveka) that leads to Self-realization.
Verse 25 of the Avadhuta Gita says:
By such sentences as “That thou art,” (Tat Tvam Asi) our own Self is affirmed. Of that which is untrue and composed of the five elements, the Sruti (scripture) says, “Not this, not this.” (Neti Neti). Therefore, by discriminating between what is Brahman and what is not, one comes to the truth. Brahman is neither the body nor the mind. Through this process, the aspirant, or yogi, soon realizes that Brahman is all, is infinite sat cit ananda (pure existence-pure consciousness-pure bliss) and attains moksha (liberation).
We can say that the affirmation “not this, not this” (neti neti) sumarizes the Advaita path, the path of discrimination.
Two well known and influential nondualist texts are the Ashtavakra Gita and Avadhuta Gita, the former said to have been written by the Sage Ashtavakra and the latter by Sage Dattatreya.
“There is only one Great Being, which the sages call Brahman, in which all the countless forms of existence reside. That Great Being is utter Consciousness, and IT is the only Essence or Self (Atman) of all beings.” -Georg Feuerstein, Sacred Paths