For the third edition of this successful undergraduate text, the author has made a number of changes to improve the presentation and clarify some of the arguments, and has also brought several of the applications up to date. The new material includes an elementary, descriptive introduction to the ideas behind the new science of chaos. The overall objectives of the book are unchanged: to lead the student to a thorough understanding of the basic concepts of vibrations and waves, to show how these concepts unify a wide variety of familiar physics, and to open doors to advanced topics which they illuminate. Each section of the book contains a brief summary of its salient contents. There are approximately 180 problems to which all numerical answers are provided, together with hints for their solution. This book is designed both for use as a text for an initial undergraduate course on vibrations and waves, and for a reference at later stages when more advanced topics or applications are met.