This book is devoted to the study of evolution of nonequilibrium systems. Such a system usually consists of regions with different dominant scales, which coexist in the spacetime where the system lives. In the case of high nonuniformity in special directions, one can see patterns separated by clearly distinguishable boundaries or interfaces. The author considers several examples of nonequilibrium systems. One of the examples describes the invasion of the solid phase into the liquid phase during the crystallization process. Another example is the transition from oxidized to reduced states in certain chemical reactions. An easily understandable example of the transition in the temporal direction is a sound beat, and the author describes typical patterns associated with this phenomenon. The main goal of the book is to present a mathematical approach to the study of highly nonuniform systems and to illustrate it with examples from physics and chemistry. The two main theories discussed are the theory of singular perturbations and the theory of dissipative systems. A set of carefully selected examples of physical and chemical systems nicely illustrates the general methods described in the book. Readership Graduate students and research mathematicians interested in differential equations, dynamical systems, and ergodic theory. Reviews "The book is well written, and the explanations are clear. ... will be an excellent introduction to the field and a valuable resource for researchers in asymptotic analysis and pattern formation in PDEs."  Mathematical Reviews "A great resource for ideas and techniques in the analysis of pattern dynamics in continuous systems ... accessible to a broad range of readers. Many examples illustrate and motivate the theory, summaries at the end of each chapter allow for reflection ... several concise proofs are given. The rich bibliography makes in depth study possible ... People interested in the theory of pattern formation should find this book instructive and inspiring reading."  Zentralblatt MATH Table of Contents  Separation and unification of scales
 Amplitude equations
 Marginal stability criterion and pattern selection
 Pattern formation
 Method of singular limit analysis
 Transient dynamics
 Future perspectives
 Bibliography
 Index
