The theory of the propagation of plane sound waves in layered structures is presented systematically in this book. The layered structures may be man-made, for example ultrasonic filters, lenses, and surface-wave delay lines, or natural media such as the ocean and the atmosphere with their marked horizontal stratification. A related problem is the propagation of elastic (seismic) waves in the earth's crust. The book retains many features and the general structure of the classic work "Waves in Layered Media" by L.M. Brekhovskikh, but also includes much new material that has not previously been treated in a monograph. Great attention is paid throughout to the physical interpretation of the results obtained. Although the subject of the book is acoustic waves, many of the interesting phenomena can be directly generalized to electromagnetic waves.