This book attempts to bridge in one step the enormous gap between introductory quantum mechanics and the research front of modern optics and scientific fields that make use of light. Hence, while it is suitable as a reference for the specialist in quantum optics, it will also be useful to the non-specialists from other disciplines who need to understand light and its uses in research. With a unique approach it introduces a single analytic tool, namely the density matrix, to analyze complex optical phenomena encountered in traditional as well as cross-disciplinary research. It moves swiftly in a tight sequence from elementary to sophisticated topics in quantum optics, including laser tweezers, laser cooling, coherent population transfer, optical magnetism, electromagnetically induced transparency, squeezed light, quantum information science and cavity quantum electrodynamics. A systematic approach is used that starts with the simplest systems - stationary two-level atoms - then introduc