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Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics. In 1996-97 the Institute for Advanced Study (Princeton, New Jersey) organized a special year-long programme designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. The purpose was to create and convey an understanding, in terms useful to mathematicians, of some fundamental notions of physics and develop the sort of intuition common among physicists for those who are used to thought processes stemming from geometry and algebra. These volumes are a written record of the programme. They contain notes from several long and many short courses covering various aspects of quantum field theory and perturbative string theory. The courses were given by leading physicists and the notes were written either by the speakers or by mathematicians who participated in the programme. The book also includes problems and solutions worked out by the editors and participants. Interspersed are mathematical texts with background material and commentary on some topics covered in the lectures.
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