**The
Friedman-Lamaitre-Robertson-Walker
metric of a homogeneous and isotropic
universe is generally agreed upon
today as the cosmological model.
However, the question of why the
observable universe is so homogeneou
and isotropic still remains an open
problem. To answer it, one must
try to analyze the possible behaviour
of space-time near a cosmological
singularity. One of the attempts at
such studies was the
Balinskii-Khalatnikov-Lifshitz
conjecture, which postulates that near
the singularity time derivatives of
the metric dominate heavily over
spatial derivaives and matter fields.
This in turn suggests consideration of
spatially homogeneous, but anisotropic
space-time models as good
approximations. **

I will begin my talk by discussing the
general structure of such space-times
and showing that their properties are
almost entirely determined by the Lie
algebra of their spatial Killing
fields. This allows them to be
classified by the Bianch
classification of the
three-dimensional Lie algebras.
Several examples of particular
physical interest will be examined in
detail - although still relatively
simple, some of these solutions of the
Einstein equations display very
untrivial properties, such as
modelling an isotropisation process or
even undergoing chaotic oscillations
when approaching the singularity.