SALIENT FEATURES OF ADVAITA VEDANTA

Three levels of truth

• The transcendental or the Pāramārthika level in which Brahman is the only reality and nothing else;
• The pragmatic or the Vyāvahārika level in which both Jiva (living creatures or individual souls) and Iswara are true; here, the material world is also true, and,
• The apparent or the Prāthibhāsika level in which material world reality is actually false, like illusion of a snake over a rope or a dream.

 Brahman

According to Adi Shankara, God, the Supreme Cosmic Spirit or Brahman (pronounced [ˈbrəh.mən]; nominative singular Brahma, Sanskrit pronunciation: [ˈbrəh.mə]) is the One, the whole and the only reality. Other than Brahman, everything else, including the universe, material objects and individuals, are false. Brahman is at best described as that infinite, omnipresent, omnipotent, incorporeal, impersonal, transcendent reality that is the divine ground of all Being. Brahman is often described as neti neti meaning "not this, not this" because Brahman cannot be correctly described as this or that. 'It' (grammatically neutral, but exceptionally treated as masculine) is the origin of this and that, the origin of forces, substances, all of existence, the undefined, the basis of all, unborn, the essential truth, unchanging, eternal, the absolute. How can it be properly described as something in the material world when itself is the basis of reality? Brahman is also beyond the senses, it would be akin a blind man trying to correctly describe color. It, though not necessarily a form of physical matter, is the substrate of the material world, which in turn is its illusory transformation. Brahman is not the effect of the world. Brahman is said to be the purest knowledge itself, and is illuminant like a source of infinite light.
Due to ignorance (avidyā), the Brahman isvisible as the material world and its objects. The actual Brahman is attributeless and formless (see Nirguna Brahman). It is the Self-existent, the Absolute and the Imperishable. Brahman is actually indescribable. It is at best "Satchidananda" (merging "Sat" + "Chit" + "Ananda", i.e., Infinite Truth, Infinite Consciousness and Infinite Bliss). Also, Brahman is free from any kind of differences or differetiation. It does not have any sajātīya (homogeneous) differentiation because there is no second Brahman. It does not have any vijātīya (heterogeneous) differentiation because there is nobody in reality existing other than Brahman. It has neither svagata (internal) differences, because Brahman is itself homogeneous.
Adi Shankara also proposed some logical proofs:

Shruti — the Upanishads and the Brahma Sutras describe Brahman in almost exact manner as Adi Shankara. This is the testimonial proof of Brahman.

Psychological — every person experiences his soul, or atman. According to Adi Shankara, Atman = Brahman. This argument also proves the omniscience of the Brahman.

Teleological/Intelligent Design — the world appears very well ordered; the reason for this cannot be an unconscious principle. The reason must be due to the Brahman.

Essential — Brahman is the basis of this created world.

Perceptible feeling — many people, when they achieve the turīya state, claim that their soul has become one with everything else