This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.Key Features: ○ The only book dealing with nonlinear waves in bounded media○ Highlights the introduction and analysis of solutions of a nonlinear difference equation — the standard mapping — that connects shocked resonance to chaos○ Introduces many concepts and publishes extensively in the literature of nonlinear waves and nonlinear resonance