By systematically covering both the Heisenberg and Schrödinger realizations, the book emphasizes the essential principles of quantum mechanics, which remain hidden within the usual derivations of the wave equation. Moreover, this presentation not only to covers the material which is traditionally presented in textbooks, but is also especially suitable for introducing the spin, i.e., the most important quantum observable. This emphasis on spin paves the way to a presentation of recent quantum-mechanical concepts such as entanglement and decoherence, and to recent applications including cryptography, teleportation and quantum computation.