1.A first course. 2.Categories and functors. 3.Semi-simplkicial complexes. 4.Ordinary homology and cohomology. 5.Spectral sequences. 6.H( BG). 7.Eilenberg-MacLane spaces and the steenroad algebra. 8.Serre’s theory of classes of abelian groups (C-theory). 9.Obstruction theory. 10.Homotopy theory. 11.Fibre bundles and topology of groups. 12.Generalized cohomology theories. 13.Final touches.