The text material in the present volume is intended as an introduction to the study of vibrations and waves in general, but the discussion is almost entirely confined to mechanical systems. Thus, except in a few places, an adequate preparation for it is a good working knowledge of elementary kinematics and dynamics. The decision to limit the scope of the book in this way was guided by the fact that the presentation is quantitative and analytical rather than descriptive. The temptation to incorporate discussions of electrical and optical systems was always strong, but it was felt that a great part of the language of the subject could be developed most simply and straightforwardly in terms of mechanical displacements and scalar wave equations, with only an occasional allusion to other systems.