Course Algebraic Topology

Algebraic topology has its initial importance in answering topological questions in terms of algebraic objects, for example in using group theory, divided into homology and homotopy. It is used in all areas in pure mathematics, and many of its constructions have counterparts in algebraic geometry as for example the étale fundamental group. As another example in number theory the universal cover is related to the maximal separable extension of a field.  So to get used to concepts in algebraic topology even helps later on to understand phenomena which are not directly coming from topology. The syllabus can be found here. 

Literature:

Allen Hatcher, "Algebraic Topology" available here.

William S. Massey, "A basic course in Algebraic Topology" 

Lectures: Mondays and Wednesdays 8:15-9:55 IMS S506

Lecture notes: Week1 Week2

Problem sheets: The problems. of the week are published on blackboard. Mainly those are problems given in the textbook.