Let n > 1 and F_n be the free group of rank n. Its automorphism group Aut(F_n) has a well-known surjective linear representation rho onto GL_n(Z). By Aut^+(F_n) := rho^(-1)(SL_n(Z)) we denote the special automorphism group of F_n. 
For an epimorphism pi  from F_n onto a finite group G we call
Gamma^+(G,pi) := {phi in Aut^+(F_n) | pi*phi = pi}
the standard congruence subgroup of Aut^+(F_n) associated to G and pi. These groups are the objects of our study, where we mainly focus on the case n=2. Our most important results are the following.
We fully describe the abelianization of Gamma^+(G,pi) for abelian and dihedral groups G. We also show that standard congruence subgroups of Aut^+(F_2) associated to dihedral groups provide a family of subgroups of Aut^+(F_2) of increasing finite index while each is generated by four elements. This implies that finite index subgroups of Aut(F_2) cannot be written as free products. Furthermore, we prove that standard congruence subgroups of Aut^+(F_2) associated to finite non-perfect groups have infinite abelianization.
We are also interested in the images of standard congruence subgroups of Aut^+(F_2) under the representation rho. For these we show that rho(Gamma^+(G,pi)) is a congruence subgroup, whenever G is a finite metacyclic group.
In the last chapter we discuss some open problems on standard congruence subgroups of Aut^+(F_2) and give suggestions for further research.