Papadopoulos A. (Ed.) Handbook of Teichmüller Theory. Volume I

European Mathematical Society, 2007. — 802 p. — (IRMA Lectures in Mathematics and Theoretical Physics 11). — ISBN 978-3-03719-029-6.In a broad sense, the subject of Teichmüller theory is the study of moduli spaces for geometric structures on surfaces. This subject makes important connections between several areas in mathematics, including low-dimensional topology, hyperbolic geometry, dynamical systems theory, differential geometry, algebraic topology, representations of discrete groups in Lie groups, symplectic geometry, topological quantum field theory, string theory, and there are others.Introduction to Teichmüller theory, old and new
Part A. The metric and the analytic theory, 1
Harmonic maps and Teichmüller theory
On Teichmüller’s metric and Thurston’s asymmetric metric on Teichmüller space
Surfaces, circles, and solenoids
About the embedding of Teichmüller space in the space of geodesic Hölder distributions
Teichmüller spaces, triangle groups and Grothendieck dessins
On the boundary of Teichmüller disks in Teichmüller and in Schottky space
Part B. The group theory, 1
Introduction to mapping class groups of surfaces and related groups
Geometric survey of subgroups of mapping class groups
Deformations of Kleinian groups
Geometry of the complex of curves and of Teichmüller space
Part C. Surfaces with singularities and discrete Riemann surfaces
Parameters for generalized Teichmüller spaces
On the moduli space of singular euclidean surfaces
Discrete Riemann surfaces
Part D. The quantum theory, 1
On quantizing Teichmüller and Thurston theories
Dual Teichmüller and lamination spaces
An analog of a modular functor from quantized Teichmüller theory
On quantum moduli space of flat PSL2(R)-connections