  Somewhat later, Weyl (1939) wrote a book, entitled The Classical  Groups, Their Invariants and Representations, in which  he returned to the theory of invariants and representations of the  semisimple Lie groups. In this work, he satisfied 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”. He intentionally restricted the discussion  of the general theory and devoted most of the book to the derivation  of specific results for the general linear, the special linear, the  orthogonal and the symplectic groups. 