  We attempt to determine the partition function of ${\cal N}=4$ super
Yang-Mills theory for $ADE$ gauge groups on $K3$ and investigate the relation
with affine Lie algebras. In particular we describe eta functions, which
compose SU(N) partition function, by level $N$ $A_{N-1}$ theta functions.
Moreover we find $D,E$ theta functions, which satisfy the Montonen-Olive
duality for $D,E$ partition functions.
