  In this paper we study the geometric structure of affine Deligne-Lusztig
varieties for $GL_3$ and $b$ basic. We completely determine the irreducible
components of the affine Deligne-Lusztig variety. In particular, we classify
the cases where all of the irreducible components are classical Deligne-Lusztig
varieties times finite-dimensional affine spaces. If this is the case, then the
irreducible components are pairwise disjoint.
