本书从流形的定义开始，探讨了流形上可能的附加结构，讨论了曲面的分类，介绍了3维流形的关键基础结果，并概述了纽结理论；然后，通过简要考虑3维流形的三角剖分、法曲面理论和Heegaard分裂，继续讨论更专业的主题。本书最后讨论了与通过曲线复合体研究3维流形的相关主题。 本书是从一门关于3维流形的研究生课程讲义发展而来的，包含约250幅插图、200多道习题，可以恰如其分地作为研究3维流形的起点，适用于有一定数学基础的对低维拓扑结构还不熟悉的读者。

前辅文
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 Sch¨onflies 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