Based on the author's longstanding course, this undergraduate-level text provides an introduction to vibration/oscillations and waves for physics, engineering, and mathematics students. Emphasizing the underlying physics and scope of applications, the book develops a unified mathematical theory of oscillations and waves in physical systems. It includes examples from the dynamics of discrete mechanical systems; continuous gases, fluids, and elastic solids; electronic circuits; electromagnetic waves; and quantum mechanical systems. The text assumes a basic familiarity with the laws of physics and standard mathematics.