This book presents a systematic introduction to the theory of parametric stability of structures under both deterministic and stochastic loadings. A comprehensive range of theories are presented and various application problems are formulated and solved, often using more than one approach. Investigation of an elastic system's dynamic stability frequently leads to the study of dynamic behavior of the solutions of parametrically excited systems. Parametric instability or resonance is more dangerous than ordinary resonance as it is characterized by exponential growth of the response amplitudes even in the presence of damping. The emphasis in this book is on the applications and various analytical and numerical methods for solving engineering problems. The materials presented are as self-contained as possible, with all of the important steps of analysis provided, in order to make the book suitable as a graduate level textbook and especially for self-study.