Begins a series publishing lecture notes presented at the Graduate Summer School at the Regional Geometry Institute in Park City, Utah. This volume explores topics from classical and quantum mechanics and field theory at a level between that of textbooks and research papers. Specifically, it contains four series of lectures: an introduction to Lie groups and symplectic geometry; introduction to quantum field theory for mathematicians; lectures on quantum mechanics and the index theorem; and lectures on axiomatic topological quantum field theory. Annotation copyright Book News, Inc. Portland, Or.