2. The role of abstract group theory in solid state physics 2.1. Isomorphism and related concepts 2.2. Group characters and product representations 2.3. Group products and invariant subgroups 2.4. Point groups, site groups and factor groups for a crystal lattice 2.5. Commuting operators; the group algebra 2.6. Double groups and magnetic groups 2.7. Symmetry groups of nonrigid molecules 3. Matrix methods and group theory . 3.1. The secular matrix and group theory . 3.2. Equivalent operators. . 3.3. The second quantization formalism 3.4. Symmetry properties for many-electron systems . 3.5. Class sum operator approach to finite group theory 3.6. Crystal field theory . 3.7. Electronic band theory . 4. Topological methods in solid state theory 4.1. Planar graphs; Euler's formula . 4.2. Topological wave functions.4.3. Connected graph expansions . 4.4. Fixed points of mappings; compound operations . 4.5. Model calculations for one-, two-and three-dimensional 4.6. Critical points for functions with lattice periodicity 4.7. The Fermi surface .
J . Killingbeckfor lattice vibrations, with particular reference to the theory of critical points in the density of states function. Finally, a survey is given of experimental methods which employ strong magnetic fields to invertigate the topology of the Fermi surface in metals.