Handbook of Teichmüller Theory, Volume VII.

Foreword
Contents
Introduction to Teichmüller theory, old and new VII
Part A. Surveys
	1. The Deligne–Mumford compactification and crystallographic groups
		1. Introduction
		2. Orbifolds and curve complexes
			2.1. Orbifolds
			2.2. Curve complexes
		3. Augmented Teichmüller spaces
		4. The ε-thick part
		5. The compactness theorem
		6. Construction of the orbifold-charts
		7. Crystallographic groups
		References
	2. Complex geometry of Teichmüller domains
		1. Introduction
		2. Preliminaries
		3. The Bers embedding
			3.1. Construction of the embedding
			3.2. Structure of the Bers boundary
		4. Invariant metrics on Teichmüller domains
			4.1. The Kobayashi and Carathéodory metrics
			4.2. Complex geodesics
			4.3. The Teichmüller metric
		5. Comparison with products and bounded symmetric domains
		6. Convexity and pseudoconvexity
		7. Kobayashi ≠ Carathéodory on Teichmüller domains
		8. Local convexity of Teichmüller domains
		References
	3. Holomorphic quadratic differentials in Teichmüller theory
		1. Introduction
		2. The co-tangent space of Teichmüller space
		3. Singular-flat geometry
		4. Extremal maps and Teichmüller geodesics
		5. Hopf differentials of harmonic maps
		6. The Hubbard–Masur theorem
		7. Schwarzian derivative and projective structures
		8. Meromorphic quadratic differentials
			8.1. Simple poles
			8.2. Poles of order two
			8.3. Higher order poles
			8.4. Meromorphic projective structures
		References
	4. Mostow strong rigidity of locally symmetric spaces revisited
		1. Introduction
		2. Deformation and rigidity of Riemann surfaces
		3. Deformation and three types of rigidity of complex manifolds
		4. Deformation and local rigidity of locally symmetric spaces
		5. Strong rigidity of lattices and locally symmetric spaces
		6. Rigidity and arithmeticity
			6.1. Local rigidity of Hermitian locally symmetric spaces and fields of definition
			6.2. Superrigidity and arithmeticity of lattices
		7. Proofs of Mostow strong rigidity
		8. Quasiconformal mappings and Mostow strong rigidity for hyperbolic manifolds
		9. The negative part of Mostow strong rigidity
		10. Generalizations of the Mostow strong rigidity
			10.1. Strong rigidity for lattices of p-adic semisimple Lie groups
			10.2. Generalizations to infinite volume locally symmetric spaces
			10.3. Rigidity results in differential geometry
		11. Other major works of Mostow and another strong rigidity
		12. Some comments on the Mostow strong rigidity
		References
	5. Models of ends of hyperbolic 3-manifolds. A survey
		1. Introduction: Fuchsian surface groups
		2. Kleinian surface groups
			2.1. Quasi-Fuchsian groups
			2.2. Laminations and pleated surfaces
			2.3. Degenerate groups
		3. Building blocks and model geometries
			3.1. Bounded geometry
			3.2. i-bounded geometry
			3.3. Amalgamation geometry
		4. Hierarchiesand the ending lamination theorem
			4.1. Hierarchies
		5. Split geometry
			5.1. Split level surfaces
			5.2. Split surfaces and weak split geometry
		References
	6. Universal Teichmüller space as a non-trivial example of infinite-dimensional complex manifolds
		1. Introduction
		2. Definition of the universal Teichmüller space
			2.1. Quasiconformal maps
			2.2. Universal Teichmüller space
			2.3. The complex structureof the universal Teichmüller space
		3. Subspaces of the universal Teichmüller space
			3.1. Classical Teichmüller spaces
			3.2. The space of normalized diffeomorphisms
		4. Grassmann realization of universal Teichmüller space
			4.1. Sobolev space of half-differentiable functions
			4.2. Grassmann realization of calT
		5. Universal Teichmüller space and string theory
			5.1. Classical system associated with smooth string theory
			5.2. Quantization of classical system (Ω_d,calA_d)
			5.3. Half-differentiable strings
			5.4. Quantization of the Sobolev space V_d
		References
	7. Generalized conformal barycentric extensionsof circle maps
		1. Introduction
		2. Generalized conformal barycentric extensions of continuous circle maps
			2.1. Definition
			2.2. Conformal naturalityand anticonformal naturality of the extension
			2.3. Continuity of the extension
			2.4. Criterion for surjectivity
		3. Qualitative and quantitative properties of the extensions of circle homeomorphisms in different classes
			3.1. Extensions of homeomorphisms
			3.2. Extensions of quasisymmetric homeomorphisms
			3.3. Extensions of locally quasisymmetric homeomorphisms
			3.4. Extensions of diffeomorphisms
		References
	8. Higgs bundles and higher Teichmüller spaces
		1. Introduction
		2. Higgs bundles
			2.1. Basic definitions
			2.2. Stability of G-Higgs bundles
			2.3. Higgs bundles and representations
		3. A basic example: G=SL(2,R)
		4. The Hitchin map, split real forms and Hitchin components
			4.1. Maximal split subgroup and Chevalley map
			4.2. The Hitchin map
			4.3. Hitchin components for SL(n,R)-Higgs bundles
			4.4. The Hitchin–Kostant–Rallis section
		5. Hermitian groups and maximal Toledo components
			5.1. Hermitian symmetric spaces and Cayley transform
			5.2. The Toledo character
			5.3. Toledo invariant and Milnor–Wood inequality
			5.4. Hermitian groups of tube type and Cayley correspondence
		6. SO(p,q)-Higgs bundles and higher Teichmüller spaces
			6.1. SO(p,q)-Higgs bundles and topological invariants
			6.2. The case 2