  A finitely presented, torsion free, abelian-by-cyclic group can always be
written as an ascending HNN extension Gamma_M of Z^n, determined by an n x n
integer matrix M with det(M) \ne 0. The group Gamma_M is polycyclic if and only
if |det(M)|=1. We give a complete classification of the nonpolycyclic groups
Gamma_M up to quasi-isometry: given n x n integer matrices M,N with |det(M)|,
|det(N)| > 1, the groups Gamma_M, Gamma_N are quasi-isometric if and only if
there exist positive integers r,s such that M^r, N^s have the same absolute
Jordan form. We also prove quasi-isometric rigidity: if Gamma_M is an
abelian-by-cyclic group determined by an n x n integer matrix M with |det(M)| >
1, and if G is any finitely generated group quasi-isometric to Gamma_M, then
there is a finite normal subgroup K of G such that G/K is abstractly
commensurable to Gamma_N, for some n x n integer matrix N with |det(N)| > 1.
