In Weyl's wonderful and terrible1 book The Classical Groups [W] one may discern two main themes: first, the study of the polynomial invariants for an arbitrary number of (contravariant or covariant) variables for a standard classical group action; second, the isotypic decomposition of the full tensor algebra for such an action.
It is largely responsible for the revival of interest in invariant theory, which had been almost killed off by David Hilbert's solution of its main problems in the 1890s.
Chapter I defines invariants and other basic ideas and describes the relation to Felix Klein's Erlangen program in geometry.
Chapter II describes the invariants of the special and general linear group of a vector space V on the polynomials over a sum of copies of V and its dual.
Chapter IV discusses Schur–Weyl duality between representations of the symmetric and general linear groups.