  We study Glois embeddings of K3 surfaces in the case where the Galois groups
are abelian. We show several properties of K3 surfaces concerning the Galois
embeddings. In particular, if the Galois group G is abelian, then G is
isomorphic to Z/4Z, Z/6Z or Z/2Z\oplusZ/2Z\oplusZ/2Z and S is a smooth complete
intersection of hypersurfaces. Further, we state the detailed structure of such
surfaces.
