This course is an introduction to topology, the study of shapes, by using algebraic constructions called “invariants”, used to determine if two differently presented topological shapes are indeed different. In this course, we show how basic topological questions may be studied by transforming them into algebraic questions and introduce the most important examples of such invariants. Topics include: homotopy, group presentations, homomorphisms, covering spaces, fundamental groups, homology groups, and, time permitting, cohomology groups along with various computations of these notions for fundamental examples and constructions of topological spaces.
