Linear and Nonlinear Instabilities in Mechanical Systems: Analysis, Control and Application is a comprehensively textbook covering analytical methods for linear and nonlinear instability phenomena in practical mechanical systems. It introduces applications of these instabilities for innovative high-performance mechanical systems and covers the fundamental mathematical theory. It begins with covering linear static and dynamics destabilization, before introducing mathematical methods which lead to nonlinear analytical methods. Reduction methods are then considered and mathematical approaches to nonlinear instability phenomena are presented. Static and dynamic instabilities in continuous systems are also covered and finally, the following applications of nonlinear instability phenomena are covered: Amplitude control of microcantilever probe in atomic force microscope (AFM), amplitude control of parametrically excited beam for mechanical filter, self-excited coupled cantilevers for ultra-sensitive mass sensor, and motion control of underactuated manipulator by bifurcation control.