This book can be used not only as a reference, but also as a graduate-level text, as it develops the subject from its foundations and contains problems and solutions for each chapter. The book begins with a discussion of vibrations in linear systems with one degree of freedom, providing a mathematical and physical basis for the subsequent chapters. Linear systems with many degrees of freedom serve to introduce the modal analysis of vibrations as well as some useful computational procedures. The book then turns to continuous linear systems, discussing both analytical solutions that provide physical insights as well as discretization techniques that supply tools for actual computation.The discussion of nonlinear vibrations includes a treatment of chaotic vibrations and other new insights. The book concludes with detailed discussions of the dynamics of rotating and reciprocating machinery. This book includes modernized notation, both the classical approach to vibration and the modern approach through dynamical systems theory, and the most recent developments in the field. To make the material accessible to students, topics are covered in a number of small and concise chapters.