Offers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more.

James J Stoker was an American applied mathematician and engineer. He was director of the Courant Institute of Mathematical Sciences and is considered one of the founders of the institute, Courant and Friedrichs being the others. Stoker is known for his work in differential geometry and theory of water waves.