  The classification of CFTs has an important subproblem, namely classifiying
the partition functions for WZW theories. This subproblem is intimately
connected to the modular behaviour of the characters of affine algebras. This
paper addresses the classification of the largest class of these -- the natural
generalization to any affine algebra of the A-series, D-series, and
$E_7$-exceptional appearing in the A-D-E classification of
Cappelli-Itzykson-Zuber for $A_1^{(1)}$. We give a programme for classifying
these for any algebra, and explicitly do this for the most interesting case:
$A_r^{(1)}$ at any level k. The exceptionals appear at (r,k)=(1,16), (2,9),
(3,8), (4,5), (7,4), (8,3) and (15,2).
