This book is a detailed look at some of the more modern issues of hydrodynamic stability, including transient growth, eigenvalue spectra, secondary instability. Analytical results and numerical simulations, linear and (selected) nonlinear stability methods will be presented. By including classical results as well as recent developments in the field of hydrodynamic stability and transition, the book can be used as a textbook for an introductory, graduate-level course in stability theory or for a special-topics fluids course. It will also be of value as a reference for researchers in the field of hydrodynamic stability theory or with an interest in recent developments in fluid dynamics. Since the appearance of "Drazin & Reid", no book on hydrodynamic stability theory has been published. However, stability theory has seen a rapid development over the past decade. Direct numerical simulations of transition to turbulence and linear analysis based on the initial-value problem are two of many such developments that will be included in the book.