Philip Holmes is Eugene Higgins Professor of Mechanical and Aerospace Engineering and Professor of Applied and Computational Mathematics, Princeton University. He works on nonlinear dynamics and differential equations. John L. Lumley is Professor Emeritus in the Department of Mechanical and Aerospace Engineering, Cornell University. He has authored or co-authored over two hundred scientific papers and several books. Gahl Berkooz leads the area of Information Management for Ford Motor Company, covering all aspects of Business Information Standards and Integration. Clarence W. Rowley is an Associate Professor of Mechanical and Aerospace Engineering at Princeton University. His research interests lie at the intersection of dynamical systems, control theory and fluid mechanics.

• Part I. Turbulence: 1. Introduction; 2. Coherent structures; 3. Proper orthogonal decomposition; 4. Galerkin projection; 5. Balanced proper orthogonal decomposition; Part II. Dynamical Systems: 6. Qualitative theory; 7. Symmetry; 8. One-dimensional 'turbulence'; 9. Randomly-perturbed systems; Part III. The Boundary Layer: 10. Low-dimensional models; 11. Behaviour of the models; Part IV. Other Applications and Related Work: 12. Some other fluid problems; 13. Review: prospects for rigor; Index.

'The book commands an impressive bibliography of 396 references, making it an invaluable reference for any researcher who wishes to get into this area of research. The authors have done the best job possible to present this work as carefully and clearly as possible. I strongly recommend the book to everyone who wishes to master this research area, as well as everyone who wants to learn more about the proper orthogonal decomposition method. The research program detailed by the authors is a very promising approach to the problem of the coherent structures of turbulence. Active turbulence researchers, especially researchers who are mainly focused in the engineering applications of turbulence, will find this book a welcome addition to their library.' Eleftherios Gkioulekas, SIAM News