Table of Contents

Preface
1: Integrability in classical mechanics
2: Soliton equations and the Inverse Scattering Transform
3: The hamiltonian formalism and the zero-curvature representation
4: Lie symmetries and reductions
5: The Lagrangian formalism and field theory
6: Gauge field theory
7: Integrability of ASDYM and twistor theory
8: Symmetry reductions and the integrable chiral model
9: Gravitational instantons
10: Anti-self-dual conformal structures
Appendix A: Manifolds and Topology
Appendix B: Complex analysis
Appendix C: Overdetermined PDEs
Index

About the Author

Maciej Dunajski read physics in Lodz, Poland and received a PhD in mathematics from Oxford University where he held a Senior Scholarship at Merton College. After spending four years as a lecturer in the Mathematical Institute in Oxford where he was a member of Roger Penrose's research group, he moved to Cambridge, where holds a Fellowship and lectureship at Clare College and a Newton Trust Lectureship at the Department of Applied Mathematics and Theoretical
Physics. Dunajski specialises in twistor theory and differential geometric approaches to integrability and solitons. He is married with two sons.

Reviews

My view is that the book is a success. I have no hesitation in recommending the book as a textbook/reference for advanced undergraduates (Mmath or other masters level), and for researchers as well. It is also very valuable as a crossover book: showing researchers in other disciplines how some of this new theory motivated by cosmology can be introduced into other areas such as fluid mechanics.
*Professor Thomas J. Bridges, Contemporary Physics*

As an introduction to an exciting area of research, this book is excellent because it is not only accessible but self contained. A wonderful feature of the book is the clear and informative explanation of the topics and the wealth of examples. The presentation style of the book means that it is accessible to readers ranging from advanced undergraduates doing research to experts. It would be an excellent textbook for a course at the advanced undergraduate level or graduate level in either mathematics or physics. This book will become a standard on the subject. The typesetting of the book is very clean, with nicely sized fonts and clean uniform notation. It includes 35 illustrations which helpfully illustrated text. It is my pleasure to highly recommend it to anyone from an advanced undergraduate to a researcher in the fields covered.
*Donald M Witt, Classical and Quantum Gravity*

While there are many exploratory texts on specific areas within the theory of integrable systems, the area has lacked a general introduction to the field. The current text takes its inspiration from mathematical physics and field theory...It does whet the reader's appetite and provides an excellent first taste of what can be savoured in detail in more advanced monographs.
*Ian A. B. Strachan, Mathmatical Reviews, issue 211b*