This book dicusses the physics of mechanical vibrating systems, emphasizing normal modes of vibration. Beginning with the basics of free and forced motions of a simple harmonic oscillator (with electrical analogs indicated where appropriate), it goes on to discuss vibrations in one-dimensional systems, such as strings and bars, and two-dimensional systems, such as membranes and plates. The discussion of coupled systems includes strong as well as weak coupling and presents both mechanical and electrical examples. The treatment includes nonlinear systems and self-excited oscillators, as well as a brief explanation of modal analysis, including finite-element methods and modal testing. The concluding third of the book discusses the propagation of sound in air, including radiation, transmission, absorption, and diffraction. The treatment of radiation covers point, dipole, line, plane, and other sources, both with and without baffles. Propagation of sound in various kinds and shapes of pipes, horns, and other acoustic components is discussed. Suitable as a text for advanced undergraduates, the book provides the foundations needed to understand the acoustics of rooms and musical instruments as well as the basics for scientists and engineers interested in noise and vibration.