The book provides an accessible overview of audio signal processing, and enables readers to design and write algorithms for the analysis, synthesis, and manipulation of musical and acoustic signals for any programming language. It provides an overview of highly interdisciplinary topics developed in a simple but rigorous way, and described in a unified and formal language which focuses on determining discrete-time audio signal models. Readers can find within a self-contained volume basic topics ranging over different disciplines: mechanical acoustics, physical systems and linear and nonlinear models, with lumped and distributed parameters; described and developed with the same level of mathematical formalism, easy to understand and oriented to the development of algorithms. Topics include the fundamental concepts of acoustic mechanics and vibration; the design of filters and equalizers for sound signals, the so-called audio effects, abstract methods of sound synthesis, and finally, methods of synthesis by physical modeling.