The contents survey the achievements and research problems connected with an adequate description of condensed matter structure, its phases and other properties in terms of appropriate mathematical tools. The focus is on the following topics: Action of groups on sets and broken symmetries; Racah-Wigner approach to vibrations, electronic states, correlations and superconductivity in multicenter systems; crystallography and its extension.

The contents survey the achievements and research problems connected with an adequate description of condensed matter structure, its phases and other properties in terms of appropriate mathematical tools. The focus is on the following topics: Action of groups on sets and broken symmetries; Racah-Wigner approach to vibrations, electronic states, correlations and superconductivity in multicenter systems; crystallography and its extension.