General Introduction.- Notations and Conventions.- Hodge Cycles on Abelian Varieties.- Tannakian Categories.- Langlands's Construction of the Taniyama Group.- Motifs et Groupes de Taniyama.- Conjugates of Shimura Varieties.- Hodge Cycles and Crystalline Cohomology.- Addendum 1989.- General Introduction.- Notations and Conventions.- Hodge Cycles on Abelian Varieties.- Tannakian Categories.- Langlands's Construction of the Taniyama Group.- Motifs et Groupes de Taniyama.- Conjugates of Shimura Varieties.- Hodge Cycles and Crystalline Cohomology.