This book addresses important aspects of nonlinear vibration analysis, presenting cases of interest to researchers and engineers. Developing the subject from its foundations, the book takes readers through vibrations in linear systems and then into nonlinear vibrations, including a treatment of chaotic vibrations. In this third edition, the classical approach to vibration and the modern approach through dynamical systems theory have been integrated; the material on control and active systems has been completely rewritten; and material relevant to mechatronics has been added.