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This text reviews the recent developments in current research connected with an adequate description of condensed matter in statistics of quasiparticals, topological invarients and self-similar structures. This book is intended for condensed matter physicists. Based on the proceedings of the 2nd International School of Theoretical Physics, the book includes the following topics: quatemions and Clifford algebra in the Euclidean group, the relativistic effective operator technique revisited, anyons and fractional statistics and phase transition and algebra of fluctuation in an exactly soluble model of a quantum anharmonic crystal.