  We prove a structure theorem for the isometry group Iso(M, g) of a compact
Lorentz manifold, under the assumption that a closed subgroup has exponential
growth. We don't assume anything about the identity component of Iso(M, g), so
that our results apply for discrete isometry groups. We infer a full
classification of lattices that can act isometrically on compact Lorentz
manifolds. Moreover, without any growth hypothesis, we prove a Tits alternative
for discrete subgroups of Iso(M, g).
