Michael Robert Herman had a profound impact on the theory of dynamical systems over the last 30 years. His seminar at the ??cole Polytechnique had major worldwide influence and was the main vector in the development of the theory of dynamical systems in France. His interests covered most aspects of the subject though closest to his heart were the so-called small divisors problems, in particular those related to the stability of quasiperiodic motions. This volume aims to reflect the depth and variety of these interests and the frontier of present research; a frontier shaped decisively by Michael Herman's contributions.

This book provides a detailed exposition of William Thurston's work on surface homeomorphisms, available here for the first time in English. Based on material of Thurston presented at a seminar in Orsay from 1976 to 1977, it covers topics such as the space of measured foliations on a surface, the Thurston compactification of Teichmuller space, the Nielsen-Thurston classification of surface homeomorphisms, and dynamical properties of pseudo-Anosov diffeomorphisms. Thurston never published the complete proofs, so this text is the only resource for many aspects of the theory.

Thurston was awarded the prestigious Fields Medal in 1982 as well as many other prizes and honors, and is widely regarded to be one of the major mathematical figures of our time. Today, his important and influential work on surface homeomorphisms is enjoying continued interest in areas ranging from the Poincare conjecture to topological dynamics and low-dimensional topology.

Conveying the extraordinary richness of Thurston's mathematical insight, this elegant and faithful translation from the original French will be an invaluable resource for the next generation of researchers and students."