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How did Shankara explain nondualism in Advaita Vedanta?

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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 philosophy of Advaita Vedanta, Shankara explains nondualism by asserting that the absolute reality, Brahman, is the only truth, while the phenomenal world and individual selves are illusory appearances.1

Shankara argues that human perception of a pluralistic world stems from avidya (ignorance) and adhyasa (superimposition), where the properties of the subject and object are mistakenly conflated. He posits that the world is not a creation or transformation of Brahman, as Brahman is immutable; rather, the world is an appearance superimposed upon it, similar to how a rope might be mistaken for a snake.12

To account for this, Shankara introduced a category of the "false" that is neither existent nor nonexistent, as it is presented in experience but sublated upon the realization of Brahman. Ultimately, the goal of life is moksha—the realization that one's own atman is identical to the nondual Brahman, thereby transcending all dualisms of the empirical world.21