Starting from basic principles, the book systematically covers both Heisenberg and Schrödinger's realizations of quantum mechanics (in this order). It provides an excellent didactic introduction to the essential principles and treats recent concepts such as entanglement and decoherence. The book gives the background needed to understand quantum cryptography, teleportation, and computation, and it is especially suitable for introducing spin. This second edition includes a more friendly presentation of Hilbert spaces, and more practical applications e.g. scanning tunneling microscope (potential barrier).