[en] Two major sections are presented. In the first, mathematical apparatus, topics covered are: basic concepts and theorems of group theory, the permutation group, groups of linear transformations, and tensor representations and tensor operators. The second section covers symmetry and quantal calculations and includes: principles of the application of group theory to quantum mechanics, classification of states, the method of coefficients of fractional parentage, and calculation of electronic states of molecular systems. A large number of tables, useful in actual calculations, is provided