This textbook is a lively and comprehensive introduction to the analysis of vibrating systems. Vibration is a branch of dynamics and is critical to safe and effective design of almost all modern industrial components. In addition to addressing this utilitarian aspect, this book takes the student on a joyous ride to explore the interesting and intriguing phenomena in vibration. The text is self-contained and starts with elementary dynamics and includes detailed derivations of discrete single and multiple degree of freedom models as well as an introduction to continuous models. MATLAB codes are integrated in the text to enable easy entry into computation. The emphases are on parametric understanding, relationship to real systems, the importance of nonlinearities that are always present in real systems, and the interpretation of analysis results. There are “think boxes” interspersed throughout the book as well as references to published papers challenging the students to go beyond the text to deepen their understanding. The approach is rigorous yet light-hearted emulating the fun-loving lecturing style the author uses in his classroom and is useful for undergraduate as well as beginning graduate students.