Ātman (Hinduism): The underlying metaphysical self, sometimes translated as spirit or soul. Ātman is a Sanskrit word that means 'inner-self' or 'soul'. In Hindu philosophy, especially in the Vedanta school of Hinduism, Ātman is the first principle, the true self of an individual beyond identification with phenomena, the essence of an individual. In order to attain liberation, a human being must acquire self-knowledge (atma jnana), which is to realize that one's true self (Ātman) is identical with the transcendent self Brahman.
The six orthodox schools of Hinduism believe that there is Ātman (Soul and Self) in every being, a major point of difference with Buddhism which does not believe that there is either soul or self.
Buddhism: Literally "self", sometimes "soul" or "ego". In Buddhism, the predominant teaching is the negating doctrine of anatman, that there is no permanent, persisting atman, and that belief in atman is the prime consequence of ignorance, the foundation of samsara.
Although the Buddha argued that no permanent, unchanging "self" can be found, some Buddhist schools, sutras and tantras present the notion of an atman or permanent "Self", although mostly referring to an Absolute and not to a personal self.
Example video: Reside in the Atman, surrender to the One, and you will know God.