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.
Quaternions and Clifford algebra in the Euclidean group, S. Altmann; Anderson localization and the integer quantum hall effect, J. Chalker; the relativistic effective operator technique revisted, R. Chatterjee and H.A. Buckmaster; finite space groups revisited, R. Dirl and B.L. Davies; the physics in rare flucturations, P.M. Duxbury; determination of space symmetries of periodic Born-Kaman crystals by the MacLane method of group extensions. W.S. Florek, et al; chaos and order in nonlinear opetical processes, K. Grygiel and P. Szlachetka; plethysms and the wreath product, A. Kerber; high-spin hydrocarbons, symmetric groups and organic ferromagnets, J. Karwowski; Cayley-dicson algebras and non-bijective canonical transformation, M.R. Kibler; anyons and fractional statistics, J.M. Leinaas; multielectron states in crystals and molecules and the duality of Weyl, T. Lulek and S. Walcerz; quantum Hall effect in periodic systems and edge states, P. Streda; geometrical frustration and its application in stability of solids, A. Szasz; berry phases - geometrical aspects, M. Szopa; quantized hall conductance as topolotical invariant, Y. S. Wu; applications of symmetric functions in physics, B.G. Wybourne; clustering matter as the ensemble of quaiparticles, A.A. Shanenko, et al; phase transitions and algebra of fluctuation operators in an exactly soluble model of a quantum anharmonic crystal, A. Verbeure.