I will introduce and discuss natural ways of assessing size of subsets of discrete groups. Some traces of these notions can be found in the work of Mitchell, Day, and Christensen. I will show that the relationships between the various ways of measuring subsets of a group depend heavily on algebraic properties of the group. Amenable, infinite conjugacy classes, and finite conjugacy classes groups will be relevant. I will present applications of these results to Haar null subsets of Polish group.