Stability is a very important property of mathematical models simulating physical processes which provides an adequate description of the process. Starting from the classical notion of the well-posedness in the Hadamard sense, this notion was adapted to different areas of research and at present is understood, depending on the physical problem under consideration, as the Lyapunov stability of stationary solutions, stability of specified initial data, stability of averaged models, etc. The stability property is of great interest for researchers in many fields such as mathematical analysis, theory of partial differential equations, optimal control, numerical analysis, fluid mechanics, etc. etc. The variety of recent results, surveys, methods and approaches to different models presented by leading world-known mathematicians, makes both volumes devoted to the stability and instability of mathematical models in fluid mechanics very attractive for provisional buyers/readers working in the above mentioned and related areas.