Simplicial and Singular Homology, 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, A Kunneth Formula, Spaces with Polynomial Cohomology, Poincar'{e} Duality, Orientations and Homology, The Duality Theorem, Connection with Cup Product, Other Forms of Duality, Universal Coefficients for Homology, The General Kunneth Formula.