This chapter is devoted to the Galois approach to solving polynomial equations.

After introducing the settings of this research, i.e. normal separable extensions K ⊃ k and the group G(K/k) of the k-automorphisms of K (Section 14.1), I discuss the correspondence between the intermediate fields F, K ⊇ F ⊇ k, and the subgroups of G(K/k); in this biunivocal correspondence, a field F corresponds to the subgroup of the k-automorphisms which leave F invariant and a group G corresponds to the subfield of the elements which are kept invariant by all the elements of G (Section 14.2), and we characterize the subgroups which are equivalent to the normal extensions F ⊃ k.