Let L/K be an abelian extension of global fields. In simple terms, the Artin reciprocity law gives an map from fractional ideals prime to discriminant to the Galois group, with an explicit kernel. This description differs a lot from classical reciprocity laws, which gives a way to compute whether a number is an n-th power mod p. We will discuss the relationship between the two, in particular in the case n = 2 and 3. Speaker(s): Angus Chung (UM)