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Nonlinear evolution equations arise in many fields of outside of mathematics including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator methods, the monotone iterative method and invariant regions, and global existence and uniqueness theory for small initial data as well as the theory and method for the study of the asymptotic behavior of solutions and global attractors. Many of the results are published in book form for the first time. Bibliographic comments in each chapter provide the reader with references and further reading materials to enable further research and study.