Topological Space: open set, closed set, compact set, limit pint, Heine-Borel Theorem, continuous map, homeomorphism, connectedness, metric space, group action on a topological space and quotient topology. Fundamental Group: loop, space of loops, homotopy, calculation of fundamental groups of some spaces, path lifting lemma, homotopy lifting lemma, fundamental groups of quotient spaces of free discrete group actions.