This book builds on the fluid and kinetic theory of equilibria and waves presented in a companion textbook, Basic Space Plasma Physics (by the same authors), but can also serve as a stand-alone text. It extends the field covered there into the domain of plasma instability and nonlinear theory.The book provides a representative selection of the many possible macro- and microinstabilities in a space plasma, from the Rayleigh-Taylor and Kelvin-Helmholtz to electrostatic and electromagnetic kinetic instabilities. Their quasilinear stabilization and nonlinear evolution and their application to space physics problems are treated. The chapters on nonlinear theory include nonlinear waves, weak turbulence and strong turbulence, all presented from the viewpoint of their relevance to space plasma physics. Special topics include auroral particle acceleration, soliton formation and caviton collapse, anomalous transport, and the theory of collisionless shocks.