Some Basic Topological Notions: Homotopy, Convexity, Contractibility, Paths and Path Connectedness Íž Fundamental group and Covering Spaces: The Fundamental Group of the circle, Induced Homomorphisms, Free Products of Groups, Seifert Van Kampen's Theorem, Covering Spaces, Lifting Properties, The Classification of Covering Spaces, Deck Transformations and Group Actions, Singular Complexes and Homology Functions, Homotopy Invariance, Exact Homology sequences, reduced homology, Excision and Mayer-Victoris sequences, Axioms for Homology.