Most physicists today accept quantum mechanics as the basis of their science. But many scientists of high renown over the past seventy years, even Einstein as late as 1955, refused to accept the theory in its entirety. From the time in 1927 when Born and Heisenberg pronounced it as "a complete theory" to as recently as 1989 when Bell charged it with dividing the world of physics, the controversy has bubbled and sometimes boiled over. The author of this book has traced the major lines of argument over those years in a most engaging style with clear descriptions of the concepts and ideas. The book can be read with a little or no background in mathematics and physics. It will be of particular interest to people who think about the philosophical underpinnings of science and its historical development. Contents: Introduction - Prologue, Part I: Atoms -Prologue, Part II: Quanta - Revolution, Part I: Heisenberg`s Matrices - Revolution, Part II: Schrödinger's Waves - Uncertainty - Complementaries - The Debate Begins - The Impossibility Thoerem - EPR - The Post-War Heresies - Bell's Theorem - Dice-Games and Conspiracies - Testing Bell - Loopholes - The Impossible Observed - Paradoxes - Philosophies - Principles - Opinions - Speculations - Postscript - Appendix - Bibliography