This book presents older classical theories of hydrodynamic stability as well as new developments in nonlinear stability, achieved mostly in the last three decades. It is designed for use by researchers and graduate students, and the author follows a fluid mechanics and applied mathematics approach. Emphasis is placed on realistic results relevant to a wide range of applications in areas such as aeronautic, chemical, civil, mechanical, environmental and oceanic engineering, geophysics, astrophysics, atmospheric sciences, naval research, oceanography and applied mathematics.

The text is divided into two main parts dealing with linear instability and nonlinear instability, while emphasis is placed on the link between theory and experimental and numerical results. Each of the five chapters included ends with problems which supplement the main text and which may be used as exercises by readers.

Contents: Fundamentals of Instability Cases and Approaches; Further Types of Instability and Applications; Nonlinear Stability; Further Topics on Nonlinear Stability; Appendices.