An introduction to the geometric and combinatorial group theory of Artin groups

We give a brief introduction to the geometric and combinatorial group theory of Artin groups. In particular we introduce the $K(\pi ,1)$ conjecture for Artin groups and survey known results as of January 2024. These notes were written as companion notes for the MFO mini-workshop 2405a “Artin groups meet triangulated categories” alongside Edmund Heng’s notes “Introduction to stability conditions and its relation to the $K(\pi ,1)$ conjecture for Artin groups”.