Theory of Groups and Its Application to Physical Problems is an introductory study of the theory of groups for persons with no easy access to an orthodox mathematical treatise on the subject. The aim is to provide an understanding of the method of applying group theory to various problems and appreciate the advantages thereof. It is hoped that this account of the theory of groups will serve a real need for physicists interested in the subject. The book opens with a discussion of the concept of groups. This is followed by separate chapters on the one-dimensional and two-dimensional lattices, some properties of groups, matrix groups, and the wave equation and its properties. Subsequent chapters deal with vibrations of a dynamical system, vibrational Raman effect and infrared absorption, molecular structure and normal modes, three-dimensional lattices, Raman and infrared spectra of crystals, crystal symmetry and physical properties, rotation groups, and applications to problems of atomic spectra.