The properties and physics of spin waves comprise an unusually rich area of research. Under the proper circumstances, these waves can exhibit either dispersive or non-dispersive propagation, isotropic or anisotropic propagation, non-reciprocity, inhomogeneous medium effects, random medium effects, frequency selective nonlinearities, soliton propagation, and chaos. This richness has also led to a number of proposed applications in microwave and optical signal processing, and spin wave phenomena are becoming increasingly important to understand the dynamics of thin-film magnetic recording heads. The book can be divided into three major parts. The first is comprised of Chapters 1-3 and is concerned with the physics of magnetism in magnetic insulators. The principal goals of these chapters are to provide a basic understanding of the microscopic origins of magnetism and exchange-dominated spin waves, motivate the equation of motion for the macroscopic magnetization, and to construct appropriate susceptibility models to describe the linear responses of magnetic materials to magnetic fields. The second part, Chapters 5-S, focuses on magnetostatic modes and dipolar spin waves, their properties, how to excite them, and how they interact with light. Chapter 4 serves as a bridge between these two parts by discussing how the susceptibility models from Chapter 3 can be used with Maxwell's equations to describe electromagnetic and magneto-quasi-static waves in dispersive anisotropic media. Finally, Chapters 9 and 10 treat nonlinear phenomena and advanced applications of spin wave excitations.