Brahman—the ultimate, transcendent and immanent God of the latter Vedas—appears as the world because of its creative energy (māyā). The world has no separate existence apart from Brahman. The experiencing self (jīva) and the transcendental self of the Universe (ātman) are in reality identical (both are Brahman), though the individual self seems different as space within a container seems different from space as such. These cardinal doctrines are represented in the anonymous verse “brahma satyam jagan mithya; jīvo brahmaiva na aparah” (Brahman is alone True, and this world of plurality is an error; the individual self is not different from Brahman). Plurality is experienced because of error in judgments (mithya) and ignorance (avidya). Knowledge of Brahman removes these errors and causes liberation from the cycle of transmigration and worldly bondage.
Modern indian philosophy has hitherto been focused on problems specific to the nation-state: modernity, integral yoga, etc. But it will be interesting to see how it grapples with new discoveries in neuroscience.
The references in classical indian literature I really admire always refer to "destroying illusion (maya)". Learning how to remove false cognition from pure sense perception. And seeing things with the vision of Brahman ;)