This course involves the study of certain geometric shapes (called topological spaces) and functions between them. The notions of a continuous function and equivalent spaces are studied in depth as well as topological properties such as connectedness, compactness, and the Hausdorff condition. The following topics may also be covered: product and quotient spaces, the separation axioms, and metric spaces. This course will use an axiomatic approach and requires a degree of comfort with abstraction and proofs. The student should be prepared for substantial writing outside of class.