This book ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations, with tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explainig theory in terms of relevant examples from real systems, this book is user- friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. The new revised and updated edition includes a new chapter on useful effects of fast vibrations and many new exercise problems.