  We introduce the notion of a diagram category and discuss its application to
the invariant theory of classical groups and super groups, with some
indications concerning extensions to quantum groups and quantum super groups.
Tensor functors from various diagram categories to categories of
representnations are introduced and their properties investigated, leading to
first and second fundamental theorems of invariant theory for classical super
groups, which include the classical groups as special cases. Application of
diagrammatic methods enables the constructionof a presentation for endomorphism
algebras for te orthogonal and symplectic groups, leading to the solution
ofproblems raised by the work of Brauer and Weyl.
