The book proposes a contemporary framework for critiquing Advaita and formulating its basic thesis in a more logical and convincing way. Any proper theory in philosophy and science has to follow from accepted assumptions. Hence the book begins by identifying basic presuppositions required for Advaita and determining the different cognitive possibilities arising out of them. After thus determining what is logically and conceptually possible and impossible in Advaita, the new framework is used to assess whether or not the traditionally held Advaitic concepts and theories are satisfactory and acceptable. This is done in many chapters covering discussions of the notions of not-Self (anātman), cosmic ignorance (māyā), individual ignorance (avidyā), illusoriness (mithyātva), sublation (bādha), entities that are different from the real and the unreal (sadasadvilaksana) and so on. The book argues that all these concepts, as specifically formulated and defended in traditional Advaita for centuries after Śankara, are simply faulty and untenable both individually and as related clusters of concepts. Traditional Advaita has also defended an elaborate ontology of experiences like mistaking a rope-for a snake. It has also heavily defended the metaphysical thesis of the empirical world of our experience being a total illusion. The logical faults and conceptual inadequacies of this ontology and metaphysics are also discussed in great detail, offering absolutely new criticisms of them. Despite this almost totally negative portrayal of traditional Advaita, the book is also quite positive in showing that any belief in non-duality is still very much philosophically possible and also necessary.