  The Vlasov-Einstein system describes a self-gravitating, collisionless gas
within the framework of general relativity. We investigate the initial value
problem in a cosmological setting with spherical, plane, or hyperbolic symmetry
and prove that for small initial data solutions exist up to a spacetime
singularity which is a curvature and a crushing singularity. An important tool
in the analysis is a local existence result with a continuation criterion
saying that solutions can be extended as long as the momenta in the support of
the phase-space distribution of the matter remain bounded.
