Table of Contents

Preliminary Concepts: Frechet Manifolds; Frechet Lie Groups; Flag Manifolds and Representations; Central Extensions and Cohomologies; Grassmannians of a Hilbert Space; Quasiconformal Maps; Loop Spaces of Compact Lie Groups: Loop Space; Central Extensions; Grassmann Realizations; Spaces of Complex Structures: Virasoro Group; Universal Techmuller Space; Quantization of Finite-Dimensional Kahler Manifolds: Dirac Quantization; Kostant-Souriau Prequantization; Blattner-Kostant-Sternberg Quantization; Quantization of Loop Spaces: Quantization of Ωℝd; Quantization of ΩTG.