This book introduces the physical background and basic concepts of vibration, mathematical modeling of linear vibrations in discrete and continuous mechanical systems and offers theoretical solutions for vibration problems, and provides dynamical analysis of vibration, engineering applications of vibration.Vibration phenomena exist widely in nature and engineering, and vibration analysis and computation are of important significance in science and in technology. In recent years, great progress has been made in vibration analysis and computation for increasingly complex systems by advances in technology. Therefore, the contents of courses on vibration should be improved and strengthened to meet the requirement of today's technology education. As an introductory textbook for undergraduate students, this book presents the physical background, mathematical modeling, analytical solutions, mechanical analysis on linear vibrations in both discrete-time and continuous-time systems, as well as some typical examples in engineering application.