Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac, and whose definitive mathematical formulation is due to von Neumann. This view, which is essentially geometric, leads most naturally to the questions of symmetry that are at the basis of all attempts to understand the world of atoms and subatomic particles. The mathematical treatment of symmetry in quantum theory is based on the theory of group representations, and this book includes a self-contained treatment of the parts of this theory which are among the most useful in quantum physics.