We study the topological notions of union and quotients of spaces; we discuss covering spaces and fundamental groups further, The notion of cell attachement is introduced and the Seifert-van Kampen Theorem is proven. Examples of surfaces illustrate the techniques.
We propose an introduction to homotopy theory for topological spaces. We define higher homotopy groups and relate them to homology groups. We introduce (co)fibration sequences, loop spaces, and suspensions. We study long exact sequences. We construct Eilenberg-Mac Lane spaces.