Preface These are the proceedings of the conference on "Quadratic Forms and Their Applications" which was held at University College Dublin from 5th to 9th July, 1999. The meeting was attended by 82 participants from Europe and elsewhere. There were 13 one-hour lectures surveying various applications of quadratic forms in algebra, number theory, algebraic geometry, topology and information theory. In addition, there were 22 half-hour lectures on more specialized topics. The papers collected together in these proceedings are of various types. Some are expanded versions of the one-hour survey lectures delivered at the conference. Others are devoted to current research and are based on the half-hour lectures. Yet others are concerned with the history of quadratic forms. All papers were refereed, and we are grateful to the referees for their work. This volume includes one of the last papers of Oleg Izhboldin, who died unex- pectedly on 17th April 2000 at the age of 37. His untimely death is a great loss to mathematics and in particular to quadratic form theory. We shall miss his brilliant and original ideas, his clarity of exposition, and his friendly and good-humoured presence. The conference was supported by the European Community under the auspices of the TMR network FMRX CT-97-0107 "Algebraic K-Theory, Linear Algebraic Groups and Related Structures". We are grateful to the Mathematics Department of University College Dublin for hosting the conference, and in particular to Thomas Unger for all his work on the TEX and web-related aspects of the conference. ix Eva Bayer-Fluckiger, Besan~on David Lewis, Dublin Andrew Ranicki, Edinburgh October, 2000
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