Algebraic topology

Content: 1 Set theory --
2 General topology --
3 Group theory --
4 Modules --
5 Euclidean spaces --
1 Homotopy and The Fundamental Group --
1 Categories --
2 Functors --
3 Homotopy --
4 Retraction and deformation --
5 H spaces --
6 Suspension --
7 The fundamental groupoid --
8 The fundamental group --
Exercises --
2 Covering Spaces and Fibrations --
1 Covering projections --
2 The homotopy lifting property --
3 Relations with the fundamental group --
4 The lifting problem --
5 The classification of covering projections --
6 Covering transformations --
7 Fiber bundles --
8 Fibrations --
Exercises --
3 Polyhedra --
1 Simplicial complexes --
2 Linearity in simplicial complexes --
3 Subdivision --
4 Simplicial approximation --
5 Contiguity classes --
6 The edge-path groupoid --
7 Graphs --
8 Examples and applications --
Exercises --
4 Homology --
1 Chain complexes --
2 Chain homotopy --
3 The homology of simplicial complexes --
4 Singular homology --
5 Exactness --
6 Mayer-Vietoris sequences --
7 Some applications of homology --
8 Axiomatic characterization of homology --
Exercises --
5 Products --
1 Homology with coefficients --
2 The universal-coefficient theorem for homology --
3 The Künneth formula --
4 Cohomology --
5 The universal-coefficient theorem for cohomology --
6 Cup and cap products --
7 Homology of fiber bundles --
8 The cohomology algebra --
9 The Steenrod squaring operations --
Exercises --
6 General Cohomology Theory and Duality --
1 The slant product --
2 Duality in topological manifolds --
3 The fundamental class of a manifold --
4 The Alexander cohomology theory --
5 The homotopy axiom for the Alexander theory --
6 Tautness and continuity --
7 Presheaves --
8 Fine presheaves --
9 Applications of the cohomology of presheaves --
10 Characteristic classes --
Exercises --
7 Homotopy Theory --
1 Exact sequences of sets of homotopy classes --
2 Higher homotopy groups --
3 Change of base points --
4 The Hurewicz homomorphism --
5 The Hurewicz isomorphism theorem --
6 CW complexes --
7 Homotopy functors --
8 Weak homotopy type --
Exercises --
8 Obstruction Theory --
1 Eilenberg-MacLane spaces --
2 Principal fibrations --
3 Moore-Postnikov factorizations --
4 Obstruction theory --
5 The suspension map --
Exercises --
9 Spectral Sequences and Homotopy Groups of Spheres --
1 Spectral sequences --
2 The spectral sequence of a fibration --
3 Applications of the homology spectral sequence --
4 Multiplicative properties of spectral sequences --
5 Applications of the cohomology spectral sequence --
6 Serre classes of abelian groups --
7 Homotopy groups of spheres --
Exercises.