This book was first published in 1999 and investigates the high
degree of symmetry that lies hidden in integrable systems. To that
end, differential equations arising from classical mechanics, such
as the KdV equation and the KP equations, are used here by the
authors to introduce the notion of an infinite dimensional
transformation group acting on spaces of integrable systems. The
work of M. Sato on the algebraic structure of completely integrable
systems is discussed, together with developments of these ideas in
the work of M. Kashiwara. This book should be accessible to anyone
with a knowledge of differential and integral calculus and
elementary complex analysis, and it will be a valuable resource to
the novice and expert alike.
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