本书从流形的定义开始，探讨流形上可能的附加结构，讨论曲面的分类，介绍3维流形的关键基础结果，并概述了纽结理论，之后简要介绍了3维流形的三角剖分、法曲面理论和Heegaard分裂等更为专业的主题，最后讨论了通过曲线复合体研究3维流形的相关主题。
本书源于一门关于3维流形的研究生课程的讲义，适合有一定数学基础但不太熟悉低维拓扑的读者阅读参考。书中包含约250幅插图和200多道习题，是学习3维流形极好的起点和概述。

Preface
Chapter 1. Perspectives on Manifolds
1.1. Topological Manifolds
1.2. Differentiable Manifolds
1.3. Oriented Manifolds
1.4. Triangulated Manifolds
1.5. Geometric Manifolds
1.6. Connected Sums
1.7. Equivalence of Categories
Chapter 2. Surfaces
2.1. A Few Facts about 1-Manifolds
2.2. Classification of Surfaces
2.3. Decompositions of Surfaces
2.4. Covering Spaces and Branched Covering Spaces
2.5. Homotopy and Isotopy on Surfaces
2.6. The Mapping Class Group
Chapter 3. 3-Manifolds
3.1. Bundles
3.2. The Schonflies Theorem
3.3. 3-Manifolds that are Prime but Reducible
3.4. Incompressible Surfaces
3.5. Dehn's Lemma*
3.6. Hierarchies*
3.7. Seifert Fibered Spaces
3.8. JSJ Decompositions
3.9. Compendium of Standard Arguments
Chapter 4. Knots and Links in 3-Manifolds
4.1. Knots and Links
4.2. Reidemeister Moves
4.3. Basic Constructions
4.4. Knot Invariants
4.5. Zoology
4.6. Braids
4.7. The Alexander Polynomial
4.8. Knots and Height Functions
4.9. The Knot Group*
4.10. Covering Spaces*
Chapter 5. Triangulated 3-Manifolds
5.1. Simplicial Complexes
5.2. Normal Surfaces
5.3. Diophantine Systems
5.4. 2-Spheres*
5.5. Prime Decompositions
5.6. Recognition Algorithms
5.7. PL Minimal Surfaces**
Chapter 6. Heegaard Splittings
6.1. Handle Decompositions
6.2. Heegaard Diagrams
6.3. Reducibility and Stabilization
6.4. Waldhausen's Theorem
6.5. Structural Theorems
6.6. The Rubinstein-Scharlemann Graphic
6.7. Weak Reducibility and Incompressible Surfaces
6.8. Generalized Heegaard Splittings
6.9. An Application
6.10. Heegaard Genus and Rank of Fundamental Group*
Chapter 7. Further Topics
7.1. Basic Hyperbolic Geometry
7.2. Hyperbolic n-Manifolds**
7.3. Dehn Surgery Ⅰ
7.4. Dehn Surgery Ⅱ
7.5. Foliations
7.6. Laminations
7.7. The Curve Complex
7.8. Through the Looking Glass**
Appendix A. General Position
Appendix B. Morse Functions
Bibliography
Index