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 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