Ideas from quantum field theory and string theory have had considerable impact on mathematics since the 1980s. Advances in many different areas have been inspired by insights from physics. In 1996-97 the Institute for Advanced Study (Princeton, USA) organized a special year-long programme designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. This is the first volume of a written record of the programme and contain notes from several long and many short courses covering various aspects of quantum field theory and perturbative string theory.

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