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<font face="Arial, Helvetica">We consider different aspects of the problem of cosmological <br /> singularity such as the BKL oscillatory approach to singularity, the <br /> new features of the cosmological dynamics in the neighbourhood of the <br /> singularity in multidimensional and superstring cosmological models and <br /> their connections with such a modern branch of mathematics as <br /> infinite-dimensional Lie algebras. Besides, we consider some new types <br /> of cosmological singularities which were widely discussed during last <br /> decade after the discovery of the phenomenon of cosmic acceleration. </font>