This book provides a concise and accessible exposition of a wide range of topics in geometric approaches to differential equations. The aim of the book is to present an overview of this developing subject and a brief introduction to a number of related topics, including twistor theory, vortex filament dynamics, calculus of variationsw, exterior differential systems and Bachklund transformations.

Written by leading experts, this book is an ideal starting point for graduate students embsrking on research. It will also be of use to researchers and anybody wishing to learn more about this burgeoning field of mathematical endeavour.

- List of Contributors
- Preface
- Introduction: Geometric Approaches to Differential Equations
- Backlund and his Works: Applications in Solition Theory
- Recent Developments in Integrable Curve Dynamics
- An Elementary Introduction to Exterior Differential Systems
- Cartan Structure of Infinite of Pseudogroups
- Cartan's Method of Equivalence
- The Inverse Problem in the Calculus of Variations and its
Ramifications
- Twistor Theory

Index