This book gives a more general discussion of quantum mechanical principles. It shows how quantum states can be represented by vectors in a vector space, with observable quantities represented by operators acting on the vectors. This formalism is used to provide a proof of the uncertainty principle and to derive quantum mechanical conservation laws. The properties of orbital and spin angular momentum are introduced and the extraordinary properties of systems of identical particles, including Bose-Einstein condensation, are explored. The book then discusses some fascinating topics in the interpretation of quantum mechanics, supported by the results of recent experiments. The process of measurement in quantum mechanics cannot be described by Schrödinger s equation and appears to involve chance in an unavoidable way. The book ends by discussing the concept of entanglement, and its applications to quantum encryption, quantum teleportation and quantum computing. The mathematical techniques used and developed in this book include vector spaces, Hermitian operators and matrix algebra.