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《代数拓扑导论(英文版)》介绍了：There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to .I.H.C. Whitehead. Of course, this is false, as a giance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details.

PrefaceTo the ReaderCHAPTER 0 Introduction Notation Brouwer Fixed Point Theorem Categories and FunctorsCHAPTER 1 Some Basic Topological Noti*** Homotopy Convexity, Contractibility, and Cones Paths and Path ConnectednessCHAPTER 2 Simplexes Affine Spaces Aftine MapsCHAPTER 3 The Fundamental Group The Fundamental Groupoid The Functor π π1(S1)CHAPTER 4 Singular Homology Holes and Green's Theorem Free Abelian Groups The Singular Complex and Homology Functors Dimension Axiom and Compact Supports The Homotopy Axiom The Hurewicz TheoremCHAPTER 5 Long Exact Sequences The Category Comp Exact Homology Sequences Reduced HomologyCHAPTER 6 Excision and Applicati*** Excision and Mayer-Vietoris Homology of Spheres and Some Applicati*** Barycentric Subdivision and the Proof of Excision Moxe Applicati*** to Euclidean SpaceCHAPTER 7 Simplicial Complexes Definiti*** Simplicial Approximation Abstract Simplicial Complexes Simplicial Homology Comparison with Singular Homology Calculati*** Fundamental Groups of Polyhedra The Seifert-van Kampen TheoremCHAPTER 8 CW Complexes Hausdorff Quotient Spaces Attaching Calls Homology and Attaching Cells CW Complexes Cellular HomologyCHAPTER 9 Natural Transformati*** Definiti*** and Examples Eilenberg-Steenrod Axioms Chain Equivalences Acyclic Models Lefschetz Fixed Point Theorem Tensor Products Universal Coefficients Eilenberg-Zilber Theorem and the Kiinneth FormulaCHAPTER 10 Covering Spaces Basic Properties Covering Transformati*** Existence Orbit SpacesCHAPTER 11 Homotopy Groups Function Spaces Group Objects and Cogroup Objects Loop Space and Suspension Homotopy Groups Exact Sequences Fibrati*** A Glimpse AheadCHAPTER 12 Cohomology Differential Forms Cohomoiogy Groups Universal Coefficients Theorems for Cohomology Cohomology Rings Computati*** and Applicati***BibliographyNotationIndex

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《代数拓扑导论(英文版)》介绍了：There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to .I.H.C. Whitehead. Of course, this is false, as a giance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details.