  We consider different aspects of the problem of cosmological singularity such
as the BKL oscillatory approach to the singularity, the new features of the
cosmological dynamics in the neighbourhood of the singularity in
multidimensional and superstring cosmological models and their connections with
such a modern branch of mathematics as infinite-dimensional Lie algebras. The
chaoticity of the oscillatory approach to the cosmological singularity is also
discussed. The Conclusion contains some thoughts about the past and the future
of the Universe in the light of the oscillatory approach to the Big Bang and
the Big Crunch cosmological singularities.
