This book highlights the fundamental principles and analytical methods of nonlinear acoustics in solids, with a focus on the theories and applications of nonlinear acoustics in ultrasonic non-destructive testing and metamaterials. The text is designed to provide readers with a deep understanding of how nonlinear acoustic phenomena manifest in various material contexts, from crystalline structures to complex composites. Suitable for readers in the fields of acoustics, materials science, and engineering, this book can advance the development of nonlinear acoustics theory and promote its applications in non-destructive testing, materials sciences, and related areas.