  This is a report on aspects of the theory and use of monoidal categories. The
first section introduces the main concepts through the example of the category
of vector spaces. String notation is explained and shown to lead naturally to a
link between knot theory and monoidal categories. The second section reviews
the light thrown on aspects of representation theory by the machinery of
monoidal category theory, such as braidings and convolution. The category
theory of Mackey functors is reviewed in the third section. Some recent
material and a conjecture concerning monoidal centres is included. The fourth
and final section looks at ways in which monoidal categories are, and might, be
used for new invariants of low-dimensional manifolds and for the field theory
of theoretical physics.
