Anatman in Advaita Vedanta
The term anatman is found not only in Buddhist sutras, but also in the writings of Adi Shankara, the founder of Advaita Vedanta. In Advaita Vedanta, this word is used to indicate Samsara - the cycle of birth, life, death and rebirth. Samsara is described as the unreal (Mithya) projected by ignorance on the real Brahman, who is the Absolute. Cosmologically, Brahman is the subtle essence that underlies phenomena, biologically, it is the supreme life-principle that gives life to the universe and psychologically, it annihilates all individualities. As Ishwara, Brahman controls both the sentient and the insentient.
The conscious existence and non-conscious existence in Brahman are both eternal. Adi Shankara calls the conscious factor Atman and the non-conscious factor as the Anatman. He does not use the term Anatman to mean non-soul or anti-soul. Atman is formless and partless. Its true nature cannot be perceived but can only be experienced. However, Anatman causes the living being to experience the pangs of (repeated) birth, suffering, old age and death. The eternal Anatman, a creation of Brahman and inseparable from it, is Mithya. The ability to discriminate Atman and Anatman leads to Moksha, liberation from the cycle of Samsara.
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