*Instructor:*Dr. Ágnes Szilárd

*Text:*Your class notes and online notes (will be available on the class homepage).

*Reference book:*Munkres: Topology, Prentice Hall, 2000

*Prerequisites*: Solid knowledge of calculus (continuous functions), basics of set theory and some group theory.

*Course description*: This is a standard introductory course the goal of which is to get acquainted with the basic notions of the field. Thus we start with point-set topology and a thorough discussion of metric and topological spaces, continuity, connectedness, compactness. We then get a glimpse of algebraic topology - the notion of the fundamental group of a topological space will be introduced and we will study covering spaces. The machinery developed will allow us to look at one of the major theorems of topology: the classification of compact, connected surfaces.

Throughout the course we will study numerous examples and applications.