This comprehensive and accessible book, now in its second edition, covers both mathematical and physical aspects of the theory of mechanical vibrations. This edition includes a new chapter on the analysis of nonlinear vibrations. The text examines the models and tools used in studying mechanical vibrations and the techniques employed for the development of solutions from a practical perspective to explain linear and nonlinear vibrations. To enable practical understanding of the subject, numerous solved and unsolved problems involving a wide range of practical situations are incorporated in each chapter. This text is designed for use by the undergraduate and postgraduate students of mechanical engineering.