This course is an introduction to Algebraic Topology. Its main topic is the study of homology groups of topological spaces. These homology groups provide algebraic invariants of topological spaces which can be computed in many examples of interest.

In the first part of the course we will construct the singular homology groups of topological spaces and establish their basic properties, such as homotopy invariance and long exact sequences. In the second part of the course we will introduce CW-complexes. These provide a useful class of topological spaces with favorable properties, and we will explain how the homology of CW-complexes can be computed using cellular homology. We will also discuss some basic concepts from homotopy theory.

**Prerequisites**

- Background in point-set topology: topological spaces, continuous maps, compactness, quotients and products, and maybe a first encounter with the fundamental group
- Knowledge about basic constructions with vector spaces and abelian groups.
- Some familiarity with categories and functors is also helpful. For those who haven't seen this before, the "Intensive course on Categories and Modules" at the start of the term is recommended.

**Rules about Homework / Exam**

There will be a written exam, with a bonus for the homework.

- Docent: Steffen Sagave