This text presents the fundamentals and applications of vibration theory. It is intended for students taking either a first course or a one-year sequence in the subject at the junior or senior level. The student is assumed to have an elementary knowledge of dynamics strength of materials and differential equations although summaries of several topics are included in the appendices for review purposes. The format of its predecessor is retained but the text material has been substantially rewritten. In view of the widespread adoption of the International System of Units (SI).by the indus- trial world SI units are used in the problems. The objectives of the text are first to establish a sense of engineering reality second to provide adequate basic theory and finally to generalize these concepts for wider applications. The primary focus of the text is on the engineering significance of the physical quantities with the mathematical structure providing a supporting role. Throughout the text examples of applications are given before the generalization to give the student a frame of reference and to avoid the pitfall of overgeneralization.