Phase Transition Dynamics This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems to establish a systematic dynamic transition theory and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields User’s Guide General Theory of Phase Transition Dynamics Dynamic Transition Theory. Equilibrium Phase Transition in Statistical Physics Fluid Dynamics Geophysical Fluid Dynamics and Climate Dynamics Dynamical Transitions in Chemistry and Biology. References