Let G be a finite group and let k be a field. Our purpose is to investigate
the simple modules for the double Burnside ring kB(G,G). It turns out that they
are evaluations at G of simple biset functors. For a fixed finite group H, we
introduce a suitable bilinear form on kB(G,H) and we prove that the quotient of
kB(-,H) by the radical of the bilinear form is a semi-simple functor. This
allows for a description of the evaluation of simple functors, hence of simple
modules for the double Burnside ring
