*Instructor:* Ágnes SZILARD PhD

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

*Prerequisites:*
Solid knowledge of calculus (limits and
continuity, manipulating with sets and fuctions) is indispensable. Rudiments of
group theory (not much more than uderstanding what the words group, subgroup,
homomorphism, isomorphism mean) will also be necessary in the second half of the
course.

*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 the study 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 as well as several ways of computing it
(using deformation retracts, covering spaces and properly discontinuous group actions).
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.