| In this mini-course we will give a brief introduction to mapping class groups, emphasizing the differences between the finite-type and infinite-type cases. For this, we will start with a reminder of surface classification and terminology, followed by basic definitions and topological properties. Then, we will review classical results for the mapping class group, including group-theoretical generation, element classification and important subgroups. Finally, we will focus on group actions and the results coming from these actions, as well as several open questions. |
