It has been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse s

Most integrable systems owe their origin to problems in geometry and they are best understood in a geometrical context. This is especially true today when the h

Twistor theory is the remarkable mathematical framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory. It h

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The boo