This volume is the fifth in a series dedicated to Teichmüller theory in a broad sense, including the study of various deformation spaces and of mapping class group actions. It is divided into four parts:
Part A: The metric and the analytic theory
Part B: The group theory
Part C: Representation theory and generalized structures
Part D: Sources
The topics that are covered include identities for the hyperbolic geodesic length spectrum, Thurston's metric, the cohomology of moduli space and mapping class groups, the Johnson homomorphisms, Higgs bundles, dynamics on character varieties, and there are many others.
Besides surveying important parts of the theory, several chapters contain conjectures and open problems. The last part contains two fundamental papers by Teichmüller, translated into English and accompanied by mathematical commentaries.
The chapters, like those of the other volumes in this collection, are written by experts who have a broad view on the subject. They have an expository character (which fits with the original purpose of this handbook), but some of them also contain original and new material.
The Handbook is addressed to researchers and to graduate students.