This second edition course text introduces the fundamental quantum physics of atoms and molecules. With revised and extended content, this book is the first volume in a series of three aiming to present a broad coverage of atomic, molecular, solid-state and statistical physics. Divided into three parts, the first provides a historical perspective leading to the contemporary view of atomic and molecular physics, outlining the principles of non-relativistic quantum mechanics. The second covers the physical description of atoms and their interaction with radiation, whilst the third deals with molecular physics. The book's pedagogical features include conceptual layout sections that define the goals of each chapter, a simplified but rigorous mathematical apparatus, and a thorough discussion of approximations used to develop the adopted physical models.