This book is a complete mathematical description of diffractions caused by seismic velocity discontinuities. Diffraction theory provides important physical insights into seismology and is a necessary part of describing the nature of a seismogram. The author describes elastic wave theory and relates it to the high-frequency approximations of ray theory. Particularly appealing to researchers interested in the development of the computer software for the seismic numerical modeling based on the ray approach, Klem-Musatov's technique is suitable for programs based on asymptotic ray theory (ART). The physics of wave propagation covered in this book should help seismologists describe seismic data with general models of the earth's interior. This book is an English translation from an earlier volume used for more than a decade by Russian seismologists.