Introductory  Paras – “The word veda comes  from the root vid,  to know. The concluding portions of the Vedas are called Upanishads or Vedanta. Vedic literature conveys, in  a poetic way, a wide spectrum of metaphysical knowledge. At the most  sublime end of the spectrum is Advaita Vedanta, which discusses the  nature of the jagat,  universe; jivas, living beings; and Brahman. The Muktika  Upanishad states:  ‘Tileshu  tailavat-veda vedantah supratishtitah;  as oil is well established in the sesame seeds, so is Vedanta in the  Vedas.’1  Advaita  Vedanta, as systematized by Acharya Shankara, is a comprehensive  science of spirituality, universally realizable and open to rational  investigation.

The  most important challenge in Advaita Vedanta is to understand the  relationship between the Atman and Brahman. A true perception of this  relationship can be acquired only by removing the veil of ignorance  caused by the upadhis,  limiting adjuncts, created by the inscrutable maya. The upadhis  manifest as the pancha-koshas,  five sheaths, which hide the real nature of the Atman. The  realization of the Atman removes all afflictions, brings eternal  knowledge, and eradicates the ego, lust, anger, attachment, hatred,  and the like. When the upadhis  are removed, the distinction between knowledge, knower, and known is  dissolved and only the Atman shines as the supreme Existence.  According to Advaita Vedanta, the realization of non-duality is the  true knowledge of the Atman, or Brahman. Acharya Shankara says:  ‘Brahma  satyam jaganmithya jivo brahmaiva naparah;  Brahman is real, the world is unreal, the jiva is non-different from  Brahman.’2

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Also read
1. Bridging Religion and Science
2. Upanishads: the science of freedom from bondage
3. Bhagavad Gita in PDF format