映射类群和Riemann曲面的模空间是2011年IAS/PCMI研究生暑期学校的主题。本书介绍了暑期学校的九个不同的讲座系列，涵盖了当前关注的一些主题。入门课程涵盖了映射类群和Teichmuller理论。高级课程涵盖了模空间的相交理论、多边形台球和模空间的动力学、映射类群的稳定上同调、Torelli群的结构和算术映射类群。
这些课程由该领域的领袖级专家提供的一系列密集的短讲座组成，旨在向学生介绍数学领域中令人兴奋的最新研究。这些讲座不重复其他地方提供的标准课程。本书为对Riemann曲面的模空间的拓扑、几何和动力学以及相关主题感兴趣的研究生和研究人员提供了一份有价值的资源。

Preface
Benson Farb, Richard Hain, and Eduard Looijenga Introduction
Yair N.Minsky
A Brief Introduction to Mapping Class Groups
1. Definitions, examples, basic structure
2. Hyperbolic geometry, laminations and foliations
3. The Nielsen-Thurston classification theorem
4. Classification continued, and consequences
5. Further reading and current events
Bibliography
Ursula Hamenstadt
Teichmuller Theory
Introduction
Lecture 1. Hyperbolic surfaces
Lecture 2. Quasiconformal maps
Lecture 3. Complex structures, Jacobians and the Weil Petersson form
Lecture 4. The curve graph and the augmented Teichmüller space
Lecture 5. Geometry and dynamics of moduli space
Bibliography
Nathalie Wahl The Mumford Conjecture, Madsen-Weiss and Homological Stability for Mapping Class Groups of Surfaces
Introduction
Lecture 1. The Mumford conjecture and the Madsen-Weiss theorem
1. The Mumford conjecture
2. Moduli space, mapping class groups and diffeomorphism groups
3. The Mumford-Morita-Miller classes
4. Homological stability
5. The Madsen-Weiss theorem
6. Exercises
Lecture 2. Homological stability: geometric ingredients
1. General strategy of proof
2. The case of the mapping class group of surfaces
3. The ordered arc complex
4. Curve complexes and disc spaces
5. Exercises
Lecture 3. Homological stability: the spectral sequence argument
1. Double complexes associated to actions on simplicial complexes
2. The spectral sequence associated to the horizontal filtration
3. The spectral sequence associated to the vertical filtration
4. The proof of stability for surfaces with boundaries
5. Closing the boundaries
6. Exercises
Lecture 4. Homological stability: the connectivity argument
1. Strategy for computing the connectivity of the ordered arc complex
2. Contractibility of the full arc complex
3. Deducing connectivity of smaller complexes
4. Exercises
Bibliography
Soren Galatius
Lectures on the Madsen–Weiss Theorem
Lecture 1. Spaces of submanifolds and the Madsen-Weiss Theorem
1.1. Spaces of manifolds
1.2. Exercises for Lecture 1
Lecture 2. Rational cohomology and outline of proof
2.1. Cohomology of Ω∞ψ
2.2. Outline of proof
2.3. Exercises for Lecture 2
Lecture 3. Topological monoids and the first part of the proof
3.1. Topological monoids
3.2. Exercises for Lecture 3
Lecture 4. Final step of the proof
4.1. Proof of theorem 4.3
4.2. Exercises for Lecture 4
Bibliography
Andrew Putman
The Torelli Group and Congruence Subgroups of the Mapping Class Group
Introduction
Lecture 1. The Torelli group
Lecture 2. The Johnson homomorphism
Lecture 3.The abelianization of Modg, n(p)
Lecture 4. The second rational homology group of Modg(p)
Bibliography
Carel Faber
Tautological Algebras of Moduli Spaces of Curves
Introduction
Lecture 1. The tautological ring of Mg
Exercises
Lecture 2. The tautological rings of Mg, n and of some natural partial compactifications of Mg, n
Exercises
Bibliography
Scott A. Wolpert
Mirzakhani's Volume Recursion and Approach for the Witten-Kontsevich Theorem on Moduli Tautological Intersection Numbers
Prelude
Lecture 1. The background and overview
Lecture 2. The McShane-Mirzakhani identity
Lecture 3. The covolume formula and recursion
Lecture 4. Symplectic reduction, principal S1 bundles and the normal form
Lecture 5. The pattern of intersection numbers and Witten-Kontsevich
Questions for the problem sessions
Bibliography
Martin Moller
Teichmuller Curves, Mainly from the Viewpoint of Algebraic Geometry
1. Introduction
2. Flat surfaces and SL2(R)-action
2.1. Flat surfaces and translation structures
2.2. Affine groups and the trace field
2.3. Strata of 2M, and hypere