The complexity of nonlinear evolution equations, the challenges of their theoretical study, and their wide-ranging applications have attracted much interest in the subject. The global existence and uniqueness, and the asymptotic behavior of solutions are the main concerns for the theoretical study of nonlinear evolution equations. Many theories and results have been developed, especially since the 1960s. However, many of them are available only in various journals. Nonlinear Evolution Equations collects those results and beginning with a review of the fundamentals, systematically explains many important and useful theories and methods for dealing with these equations. 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. The final chapter explores the asymptotic behavior of solutions and global attractors, presenting a number of more recent results never before published in book form. The applications of nonlinear evolution equations reach from mathematical physics and mechanics to materials science and even the biological sciences. With its clear, concise explanations, Nonlinear Evolution Equations builds the background students of mathematics and researchers across the spectrum of nonlinear science needs to prepare for applications and for further advances in the field.