Introduction
Chapter 1 The fundamental group and some of its applications
1.What is algebraic topology?
2.The fundamental group
3.Dependence on the basepoint
4.Homotopy invariance
5.Calculations: π1 (R) =0 and π1 (S1) = Z
6.The Brouwer fixed point theorem
7.The fundamental theorem of algebra
Chapter 2 Categorical language and the van Kampen theorem
1.Categories
2.Functors
3.Natural transformations
4.Homotopy categories and homotopy equivalences
5.The fundamental groupoid
6.Limits and colimits
7.The van Kampen theorem
8.Examples of the van Kanpen theorem
Chapter 3 Covering spaces
1.The definition of covering spaces
2.The unique path lifting property
3.Coverings of groupoids
4.Group actions and orbit categories
5.The classification of coverings of groupoids
6.The construction of coverings of groupoids
7.The classification of coverings of spaces
8.The construction of coverings of spaces
Chapter 4 Graphs
1.The definition of graphs
2.Edge paths and trees
3.The homotopy types of graphs
4.Covers of graphs and Euler characteristics
5.Applications to groups
Chapter 5 Compactly generated spaces
1.The definition of compactly generated spaces
2.The category of compactly generated spaces
Chapter 6 Cofibrations
1.The definition of cofibrations
2.Mapping cylinders and cofibrations
3.Replacing maps by cofibrations
4.A criterion for a map to be a cofibration
5.Cofiber homotopy equivalence
Chapter 7 Fibrations
1.The definition of fibrations
2.Path lifting functions and fibrations
3.Replacing maps by fibrations
4.A criterion for a map to be a fibration
5.Fiber homotopy equivalence
6.Change of fiber
Chapter 8 Based cofiber and fiber sequences
