These are notes (taken by E. Vitale) of a summer school held at the University of Bologna in the week of 22-26 May, 2023 as part of the program Quiver Representations, Quiver Varieties and Combinatorics. This is the announcement for the course. Counting representations of quivers over finite fields In these lectures I will present the calculation of the title in the case of the star-shaped quivers related to character varieties based on my joint work with E.