  We analyze the global dynamics of Bianchi type I solutions of the Einstein
equations with anisotropic matter. The matter model is not specified explicitly
but only through a set of mild and physically motivated assumptions; thereby
our analysis covers matter models as different from each other as, e.g.,
collisionless matter, elastic matter and magnetic fields. The main result we
prove is the existence of an `anisotropy classification' for the asymptotic
behaviour of Bianchi type I cosmologies. The type of asymptotic behaviour of
generic solutions is determined by one single parameter that describes certain
properties of the anisotropic matter model under extreme conditions. The
anisotropy classification comprises the following types. The convergent type
\Aplus: Each solution converges to a Kasner solution as the singularity is
approached and each Kasner solution is a possible past asymptotic state. The
convergent types \Bplus and \Cplus: Each solution converges to a Kasner
solution as the singularity is approached; however, the set of Kasner solutions
that are possible past asymptotic states is restricted. The oscillatory type
\Dplus: Each solution oscillates between different Kasner solutions as the
singularity is approached. Furthermore, we investigate non-generic asymptotic
behaviour and the future asymptotic behaviour of solutions.
