Abstract
Suppose phi is a Drinfeld A-module over K and Λ(Q, phi) is the Q-torsion points of phi in Ks. We want to know the Galois group Gal(K(Λ(Q, phi))/K). In this thesis, we will consider the case K is a local field containing a global function field F and phi is of low rank, and give an explicit description about the representation of Gal(Ks/K) on Λ(Q, phi). For the purpose, we will adapt Serre's methods for studying the Galois representation on the torsion points of formal groups and elliptic curves. We will consider the case F=Fq(t),A=Fq[t] and phi of rank 1 and 2. We will also study the case of general Drinfeld A-modules of rank 1.