Water wave motion has been studied in great detail for many years. There are many reasons for this attention; examples include the construction of bridges over rivers and the erection of coastal defenses designed to protect harbors from the effects of the sea. The need for mathematical models to determine wave motion in such situations is of vital importance as bad choices of location for these constructions could be extremely hazardous. This book considers the use of mild-slope models to approximate the effects of varying depth topography on water wave motion. The original mathematical problem is reformulated in terms of a pair of real-valued integral equations and solution techniques are discussed. Finally numerical examples are included which show that this solution method compares very favorably with more established algorithms. This work will be of interest to students studying water wave motion and / or integral equations as it discusses the solution of a real world problem using a blend of classical and modern techniques. More established researchers in the field of fluid mechanics may therefore be interested in the work presented here.