This volume reviews some selected problems in solid state physics with an emphasis on adequate mathematical tools. The three main subjects covered are: magnetic structures and neutron scattering; Berry phases and energy bands in solids (symmetry, analicity, Hofstadter butterfly, van Hove singularities); and quasicrystals, finite systems, and group action on sets (unitary group approach, Schur functions).
Wigner's theorem for non-unitary symmetry groups, J. Kocinski; quantum group structure of Hofstadter model, A. Zabrodin; interaction mechanisms for holes in the Hubbard-Anderson model for high-Tc superconductivity, W.J. Caspers; alternative classification schemes of space group representations - applications to physical problems, R. Dirl; use of the Braid group for anyons on various manifolds and connection to the fractional quantum Hall effect, T. Einarsson; the 3-dim lattices, up to dilations and orthogonal transformations (i.e. their position) from a 5-dimensional orbifold, L. Michel; medium-range order in planar atomic arrangements with fivefold symmetry, J.C.S. Levy; unitary group invariants and finite systems, J. Karwowski; a quasi-crystal model based on the fibre-bundle theory, M. Krichevets; the determination of the orbit spaces of compact coregular linear groups, V. Talamini; superconductors in quantizing magnetic fields, L. Kowalewski; solid C60 - structure and lattice dynamics at low temperature, V.A. Andreev et al; two-dimensional Heisenberg lattices, P. Moustanis. (Part contents).