Elements of General Topology. Quotient topology. Concise introduction to topological manifolds and the classification of
compact surfaces. Group actions on topological spaces with emphasis on even actions. Homotopy of maps.
Fundamental group of a topological space. Homotopy equivalence. Simply connected spaces. Contractible spaces.
Fundamental groups of retractions. Coverings. Lifting of homotopy. Monodromy. Homomorphism of fundamental
groups induced by covering. Semilocally simply connected spaces. Universal covering spaces. Introduction to singular
homology. Survey of important results in Algebraic Topology: Invariance of dimension, Hairy Ball Theorem, Brouwer
fixed point Theorem, Invariance of domain, Jordan-Brouwer Theorem.