In 2009 T. Ekedahl introduced some cohomological invariants for a finite group G. These relate, naturally, to invariant theory for groups and, also, to the Noether's Problem (one wonders about the rationality of the extension F(G) = F(x_g: g in G)^G over F, for a field F and a finite group G). In this talk, we introduce these invariants and we highlight some results.