This book presents current research trends in the field of underwater acoustic wave direct and inverse problems. The ocean-seabed system is an acoustic waveguide, and this is the only book that treats inverse problems in a waveguide. The propagation of acoustic waves in this system is treated for various types of seabeds and the direct and inverse problems are considered in realistic ocean environments. The inverse problem is to determine the shape of an impenetrable or penetrable object, or to determine the coefficients describing the seabed, achieved by acoustically illuminating the seabed and investigating the scattered field. The book emphasizes computation of Green's Functions with new material added for elastic and poro-elastic seabeds. It addresses many areas of practical interest related to underwater acoustical imaging, including ecological survey and cleanup, protection of open water harbors, maintenance of offshore petroleum and gas enterprises, and other areas of environmental and military concern.