**Time and place:** Tuesday (first session: January 31), 10.30-12.30, room: HG 03.054

Questions about the exercises (and also the lecture) can be discussed with Matija Bašić and Giovanni Caviglia (room: HG 03.064) each Wednesday from 11.00 to 12.00. Grades will be given based on a presentation at the end of the lecture and an oral examination.

**Lecture notes (updated course notes and exercise sheets can be found here):**

Lecture 01 Definition of singular homology, first examples

Lecture 02 Low-dimensional identifications

Lecture 03 Some homological algebra, relative singular homology

Lecture 04 Chain homotopies, singular homology of contractible spaces

Lecture 05 Homotopy invariance of singular homology

Lecture 06 Excision property and Mayer-Vietoris sequence

Lecture 07 Proof of excision property of singular homology

Lecture 08 Jordan-Brouwer separation theorem

Lecture 09 Degree of a map, CW-complexes

Lecture 10 CW-complexes and cellular homology

Lecture 11 no regular lecture, presentation of projects to students

Lecture 12 Isomorphism between cellular and singular homology

**Projects to be presented by students:**

Project 1: Simplicial sets and the geometric realization

Project 2: Homology with coefficients and universal coefficient theorem

Project 3: Galois theory of covering spaces