In the early 70's and 80's the field of integrable systems was in its
prime youth: results and ideas were mushrooming all over the world. It
was during the roaring 70's and 80's that a first version of the book
was born, based on our research and on lectures which each of us had
given. We owe many ideas to our colleagues Teruhisa Matsusaka and David
Mumford, and to our inspiring graduate students (Constantin
Bechlivanidis, Luc Haine, Ahmed Lesfari, Andrew McDaniel, Luis Piovan
and Pol Vanhaecke). As it stood, our first version lacked rigor and
precision, was rough, dis- connected and incomplete. . . In the early
90's new problems appeared on the horizon and the project came to a
complete standstill, ultimately con- fined to a floppy. A few years ago,
under the impulse of Pol Vanhaecke, the project was revived and gained
real momentum due to his insight, vision and determination. The leap
from the old to the new version is gigantic. The book is designed as a
teaching textbook and is aimed at a wide read- ership of mathematicians
and physicists, graduate students and professionals.