Includes bibliographical references (p. 357-367) and index.

Quasiconformal mapping Riemann surfaces Quadratic differentials, Part I Quadratic differentials, Part II Teichmuller equivalence The Bers embedding Kobayashi's metric on Teichmuller space Isomorphisms and automorphisms Teichmuller uniqueness The mapping class group Jenkins-Strebel differentials Measured foliations Obstacle problems Asymptotic Teichmuller space Asymptotically extremal maps Universal Teichmuller space Substantial boundary points Earthquake mappings Bibliography Index.

The Teichmuller space (X) s the space of marked conformal structures on a given quasi conformal surface . This volume uses quasi conformal mapping to give a unified and up-to-date treatment of (X) Emphasis is placed on parts of the theory applicable to non compact surfaces and to surfaces possibly of infinite analytic type. The book provides a treatment of deformations of complex structures on infinite Riemann surfaces and gives background for further research in many areas. These include applications to fractal geometry, to three-dimensional manifolds through its relationship to Kleinian groups, and to one-dimensional dynamics through its relationship to quasi symmetric mappings. Many research problems in the application of function theory to geometry and dynamics are suggested.