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How did the Upanishads relate brahman to atman?

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Indian philosophy In the Bhagavad Gita Arjuna and the Hindu deity Krishna, who also serves as Arjuna's charioteer (as depicted in this 17th-century illustration), engaging in a philosophical dialogue.

In the Upanishads, the relationship between brahman (the Absolute Reality) and atman (the innermost self) is defined by their fundamental identity. The Upanishads resolve the question of the ultimate nature of being by establishing the equation brahman = atman.12

This identification serves as a cornerstone of Indian philosophy, particularly within the Vedanta school. By equating the Absolute that underlies the universe with the innermost core of the human person, the Upanishads spiritualized the concept of the Absolute and universalized the concept of the self. This profound connection is famously expressed in the phrase "tat tvam asi" ("Thou art that"), which signifies that the individual self is, in reality, the supreme reality.1324

While various teachers offered different explications—ranging from negative descriptions (neti neti, "not this, not this") to positive affirmations of all-pervasiveness—the core teaching remains that the self is not separate from the Absolute. Realizing this identity is considered essential for achieving moksha, or spiritual release.231