"This is a thought-provoking book. Mirman is a crusader for the advancement of a no-nonsense approach to physics. He does not request your complete agreement, but your willingness to think, which is good. I enjoyed the ride." David J. Santos, Mathematical Reviews In-depth analysis of the necessity for quantum mechanics and for its properties. All are (easily) understandable and unavoidable. Geometry, group theory and consistency require wavefunctions (group basis vectors) and that nature be probabilistic. Absolute values for experiments follow. Probability is defined. Reasons for confusion and misunderstandings are analyzed; much are based on misuse of (what is often not) language. These are extirpated. It is shown why (not only) the Einstein, Podolsky, Rosen paradox, uncertainty principles, the vacuum, are so thoroughly misunderstood. Quantum mechanics is local (with no spookiness) and requires the vacuum be empty. Reality is mathematical.