We focus on a development of the group- theoretical methods and their application in the physics of low-dimensional systems. We study band structure, optical conductivity, plasmon excitations, Raman spectra, mechanical properties, electric and thermal transport, spin magnetic orderings etc. of low-dimensional systems like carbon and inorganic nanotubes, helical carbon nanotubes, graphene, polymers, and DNA, critical behavior and avalanches in ferromagnets, Barkhausen noise theory and experiment, kinetic models and simulations in gas discharges. We have developed a POLSym software package which can be used in polymer and nanotube research by scientists who are non-specialists in the group theory.