The book, as its title suggests, is devoted to the physical applications of group theory. The book is based on lectures given by the author, American physicist Morton Hamermesh, for employees of one of the major scientific centers of the United States-Argonne National Laboratory. The author has consistently and clearly outlined the foundations of group theory and its most important for applications section-theory of representations .. The applications of group theory to numerous physical problems (crystal and molecular symmetry, magnetic symmetry, atomic spectra, nuclear and elementary particle physics, etc.) are discussed in detail. ). The concepts and concepts introduced and the results obtained are illustrated with numerous examples, interesting tasks and exercises are given. The book is designed primarily for students and graduate students specializing in various fields of theoretical physics; it will also be useful for scientists - physicists and chemists who want to master the theory of groups. Finally, the book will attract the attention of mathematicians interested in the physical applications of group theory.