Discover the math behind water waves and how it explains phenomena from shorelines to ships at sea. This authoritative introduction surveys the broad field of surface gravity waves, blending physical intuition with mathematical rigor. It explains how a wide range of problems—from waves on beaches and river floods to ship motion and atmospheric fronts—fit into a unified framework. The book builds from fundamental hydrodynamics to advanced topics, balancing theory with real-world applications. Four main parts guide the reader: the basic theory for non-viscous fluids; a linear theory for small-amplitude waves; nonlinear shallow-water theory for long waves; and the exact nonlinear free-surface theory. Along the way, it covers essential tools such as potential theory, conformal mapping, Green’s functions, and integral equations, and shows how these methods illuminate both classical problems and modern computational approaches. Broad coverage of physical problems, including storm waves, beach diffusion, ship motion, and flood waves in rivers. - A clear path from the foundational equations to practical analysis and numerical methods. - Emphasis on a self-contained presentation that connects physics with the mathematics used to solve it. - Guidance on reading portions independently, with careful attention to physical assumptions and mathematical conclusions. Ideal for readers with interests in engineering, hydrodynamics, and physical oceanography who want a solid, readable guide to surface wave problems and their solutions.