Introduction to the theory of the free transition-metal atoms and ions, having a partly filled d-shell. Thereafter, these are placed in crystals or inorganic complexes. Here the theory of point groups is of interest. Both the ligand field and the crystal field theories will be explained. The level of the intended lecture is about the same as the book by Cotton: ‘Chemical applications of Group Theory’. It is amazing to see how intricate problems can be simplified by group theory. Applications related to the ligand field theory, but also to vibrations and molecular orbitals, will be treated.