"Until now, there has been no equivalent treatment of seismic diffraction theory in the Western literature" (L.Lines). 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. Klem-Musatov describes elastic wave theory and relates it to the high frequency approximations of ray theory. This book is particularly appealing to researchers interested in the development of the computer software for the seismic numerical modeling based on the ray approach. Klem-Musatovs's technique is suitable for programs based on Asymptotic Ray Theory (ART). Another important asset of this book is in its many numerical examples, which illustrate practical implementation of the Klem-Musatov method and considerably elucidate its theoretical exposition by the author. The physics of wave propagation covered in this book should help the seismologist to describe seismic data with general models of the Earth's interior. This book is an English translation from an earlier volume used for over a decade by Russian seismologists.