The book introduces the existence, uniqueness, regularity and the long time behavior of solutions with respect to space and time, and the explosion phenomenon for some evolution equations, including the KdV equation, the nonlinear Schrödinger equation, the sine-Gordon equation, the Zakharov equations, the Landau-Lifshitz equations, the Boussinesq equation, the Navier-Stokes equations and the Newton-Boussinesq equations etc., as well as the basic concepts and research methods of infinite-dimensional dynamical systems. This book presents fundamental elements and important advances in nonlinear evolution equations. It is intended for senior university students, graduate students, postdoctoral fellows and young teachers to acquire a basic understanding of this field, while providing a reference for experienced researchers and teachers in natural sciences and engineering technology to broaden their knowledge.