This book is concerned with wave propagation in reacting media, specifically in electromagnetic materials. A clear and systematic account is presented of the mathematical methods of wave phenomena in electromagnetic materials, which will be readily accessible to physicists and engineers. Chapter 1 presents the theory of time-varying electromagnetic fields, which involves a discussion of Feraday's laws, Maxwell's equations and their application to electromagnetic wave propagation under a variety of conditions. Chapter 7 is concerned with a discussion of magnetohydrodynamics and plasma physics. Special survey chapters are included on quantum mechanics and the theory of relativity. The mathematical foundation of electromagnetic waves vis à vis partial differential equations is contained in chapters 2 and 3. Chapters 4 and 5 present variational methods and Hamilton Jacobi theory which are essential to a deeper understanding of modern concepts in wave propagation and quantum mechanics.