The talk can be treated as an invitation to the finiteness properties of groups. I will start with the basic notion of group and discuss the meaning of a group being finitely generated and finitely presented.  Then I will discuss the natural high dimensional analog of these and give an overview on the finiteness properties of groups. In particular, we will highlight some major problems in the area. If time permited, I will also discuss some of my recent joint work with Javier Aramayona, Kai-Use  Bux, Jonas Flechsig and Nansen Petrosyan.

5.6.pdf