Simplicial Homology, Singular Homology, Homotopy Invariance, Exact Sequences and Excision, The Equivalence of Simplicial and Singular Homology, Computations and Applications, Degree, Cellular Homology, Mayer-Vietoris Sequences, Homology with Coefficients. Cohomology Groups, The Universal Coefficient Theorem, Cohomology of Spaces, Cup Product, The Cohomology Ring, Künneth Formula, Spaces with Polynomial Cohomology, Poincaré Duality, Orientations and Homology, The Duality Theorem, Connection with Cup Product, Other Forms of Duality, Universal Coefficients for Homology, The General Künneth Formula.