  The aim of this lecture is to present the concept of C-algebra and to
illustrate its applications in two contexts: the study of reflection groups and
their folding on the one hand, the structure of rational conformal field
theories on the other. For simplicity the discussion is restricted to finite
Coxeter groups and conformal theories with a $\hat{sl}(2)$ current algebra, but
it may be extended to a larger class of groups and theories associated with
$\hat{sl}(N)$. (Proceedings of the RIMS Symposium, Kyoto, 16-19 December 1996.)
