1.Axioms and general theorems. 2.Simplical somplexes. 3.Homology theory of simplical complexes. 4.Categories and functors. 5.Chain complexes. 6.Formal homology theory of simplicial complexes. 7.The singular homology theory. 8.Systems of groups and their limits. 9.The Cech homology theory. 10.Special features of the Cech theory. 11.Applications to Euclidean spaces.