  This newly acquired appreciation of group theory led Weyl to what he  himself considered his greatest work in mathematics, a general theory of the representations and invariants of the classical Lie groups  (Weyl 1924a, 1924f, 1925, 1926a, 1926b, 1926c). Later Weyl (1939)  wrote a book, The Classical Groups: Their Invariants and  Representations, in which he returned to the theory of  invariants and representations of semisimple Lie groups. In this work he realized his ambition “to derive the decisive results for  the most important of these groups by direct algebraic construction,  in particular for the full group of all non-singular linear  transformations and for the orthogonal group.”