Let F-2 be the free group of rank two, and Phi 2 its automorphism grou
p. We consider the problem;of describing the representations of Phi(2)
of degree n for small values of n. Our main result is the classificat
ion (up to equivalence) of all indecomposable representations rho of P
hi(2) of degree n less than or equal to 4 such that rho(F-2) not equal
1. There are only finitely many such representations, and in all them
rho(F-2) is solvable. This is no longer true in higher dimensions. Al
ready for n = 6 there exists a 1-parameter family of irreducible noneq
uivalent representations of Phi(2) such that rho(F-2) contains a free
non-abelian subgroup. We also obtain some new 4-dimensional representa
tions of the braid group B-4 which are indecomposable and reducible at
the same time. It would be interesting to find some applications of t
hese representations.