The basic definitions and theorems of group theory, which are used in the standard theory of the electronic structure of atoms in a crystal field and molecules, are briefly considered in this chapter. Particular attention is paid to the methods for constructing two-electron states and wavefunctions in multicenter systems. To consider the spin parts of the wavefunctions, instead of the standard approach of double groups, the method of projective representations is used. The application of the approaches is illustrated by many examples of the construction of electron states in point group symmetry.