Essential Advanced Physics is a series comprising four parts: Classical Mechanics, Classical Electrodynamics, Quantum Mechanics and Statistical Mechanics. Each part consists of two volumes, Lecture notes and Problems with solutions, further supplemented by an additional collection of test problems and solutions available to qualifying university instructors. This volume, Quantum Mechanics: Lecture notes, is intended to be the basis for a two-semester, graduate-level course. It starts with coverage of numerous wave-mechanical effects in one- and multi-dimensional systems (including the energy band theory), and then proceeds to the bra-ket formalism necessary for the discussion of more advanced topics, including particle spin, and open and multi-particle quantum systems. The book also includes a section on quantum computation and cryptography, and it ends with a special chapter on quantum measurements and interpretations of quantum mechanics.