• 1. The Evolution of Evolutionary Equations.- 2. Dynamical Systems: Basic Theory.- 3. Linear Semigroups.- 4. Basic Theory of Evolutionary Equations.- 5. Nonlinear Partial Differential Equations.- 6. Navier-Stokes Dynamics.- 7. Major Features of Dynamical Systems.- 8. Inertial Manifolds: The Reduction Principle.- Appendices: Basics of Functional Analysis.- A Banach Spaces and Fréchet Spaces.- B Function Spaces and Sobolev Imbedding Theorems.- C Calculus of Vector-Valued Functions.- D Basic Inequalities.- E Commentary.- Notation Index.

From the reviews: "The book under review is a fundamental introduction into the field of infinite-dimensional dynamical systems, especially those generated from evolutionary partial differential equations. It is addressed to all those who embark on their journey into this fascinating topic ... . the book is nicely written, there are given useful commentaries on all steps and to original and surrounding works. It can be highly recommended to all those who wish to enjoy the world of dynamics of evolutionary equations." (J. Synnatzschke, Zeitschrift fur Analysis und ihre Anwendungen, Vol. 21 (3), 2002) "The dynamics of evolutionary equations are a nice example of the interaction between the theory of ordinary and of partial differential equations. The present volume is a significant contribution to this theory, and should become soon a reference book. ... The book can undoubtedly be recommended and used as a basis for graduate courses in partial differential equations, as well as a reference volume for researchers in the important area of evolutionary equations." (Jean Mawhin, Bulletin of the Belgian Mathematical Society, Vol. 11 (4), 2004) "Two well-known experts are the authors of this book on the theory and applications of infinite dimensional dynamical systems. ... Some basic results from functional analysis are included in the Appendices. This makes the book self-contained. ... The whole text is very carefully written. This excellent book will be certainly a basic reference on infinite dimensional dynamical systems. I can recommend it to researchers and graduate students in mathematics, physical sciences, and engineering." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 69, 2003) "The present book gives an introduction to infinite-dimensional dynamical systems suitable for graduate students with a solid background from functional analysis. ... It is well-written and contains many results which are otherwise hard to find in the text book literature." (G. Teschl, Monatshefte fur Mathematik, Vol. 138 (3), 2003)