ABSTRACT
The group theory emerged from several branches of mathematics: the numbers theory, geometry, and algebraic equations. The foundations of group theory were developed by L. Euler, C. F. Gauss, N. H. Abel, E. Galois, and many other prominent mathematicians. In chemistry the group theory facilitates description of various properties of molecules and symmetry properties of molecular orbitals. In physics importance of group theory follows from the fact that the symmetry properties of a considered physical system are related to the laws of conservation of certain physical quantities. The set of the symmetry elements of an object forms a group, and this is a very important observation that allows to apply the group theory formalism to describe the symmetry properties of various objects. The group theory provides us with a unified approach to deal with the spectroscopic problems, for example, classification of the energy levels of impurity ions in crystals, selection rules for allowed transitions, analysis of vibrations of molecules, etc.
