On the motivic galois group of a number field

In this thesis, it is proved that there is a homomorphism from Weil-Arthur idele group to Taniyama group, which is isomorphic to the motivic Galois group of CM motives. Furthermore if James Arthur's construction of Langlands' group is valid, and the group G_F that he constructs is indeed isomorphic to the motivic Galois group then there is a commutative diagram that these groups fit inside. In order to lay the foundations for these groups, there is a review of (i) category theory, (ii) algebraic geometry, (ii) Tannakian categories, (iii) motives and motivic Galois group, (iv) Alexander Grothendieck's standard conjectures, (v) Weil group and Artin Reciprocity of number theory, (vi) construction of Serre-Taniyama group, (vii) James Arthur's construction of Langlands' group, (vii) Complex Multiplication, Abelian Varieties, and CM motives.