  Using shift vector method we obtain a large class of self-dual lattices of
dimension $(l,l)$, which has a one to one correspondence with modular
invariants of free bosonic theory compactified on co-root lattice of a rank $l$
Lie group. Then a large number of modular invariants of affine Lie algebras are
derived explicitly. As two applications of this method, we give a direct
derivation of $D$-series of $SU(N)$ and a new proof for the A-D-E
classification of the $SU(2)_k$ partition functions.
