We obtain a number of analogues of the classical results of the 1960s on the general linear groups GLn(Z) and special linear groups SLn(Z) for the automorphism group ΓA = Aut(A) of an infinitely generated free abelian group A. In particular, we obtain a description of normal generators of the group Aut(A), classify the maximal normal subgroups of the group Aut(A), describe normal generators of the principal congruence subgroups ΓA(m) of the group Aut(A), and obtain an analogue of Brenner's ladder relation for the group Aut(A).