This reprint differs from the original one (published in 1968 see Zbl 0186.25701) by the inclusion of short notes giving references to new results, and by a supplementary bibliography which does not claim to be complete. The author gives in the special preface for this reprint-edition some hints about new developments in the field of \(\ell\)-adic representations especially in connection with (1) abelian varieties over number fields, (2) modular forms, and (3) local ground fields.