Formal groups are easily de ned algebraic objects that have a wide range of applications in many eld of mathematics from cobordism theory to number theory with the present talk being devoted to the latter. They are de ned as formal power series F in two variables such that F(x; 0) = x; F(F(x; y); z) = F(x; F(y; z)) and F(x; y) = F(y; x). A relation between formal groups and reciprocity laws is investigated following the approach by Honda. Let  denote an m-th primitive root of unity. For a character  of order m, we de ne two one-dimensional formal groups over Z[] and prove the existence of an integral homomorphism between them with linear coecient equal to the Gauss sum of . This allows us to deduce a reciprocity formula for the m-th residue symbol which, in particular, implies the cubic reciprocity law.