The  reduction  problem for representations
of  affine  Lie  algebras  to  that  of  affine
subalgebra   is   considered.   The   universal
recurrent  relation  for branching coefficients
is  proved.  This relation is used to construct
the  algorithm for the reduction procedure. The
branching  problem  for  affine algebra modules
appears  in  the  Wess-Zumino-Witten  models of
two-dimensional  conformal  field theory, where
it  is  used  to  construct  the  model  on the
higher-genus  Riemann surfaces. The formulation
of  a  conformal  field  theory on higher genus
surfaces  is  important for the study of string
interactions    and    the    description    of
two-dimensional   systems   near  the  critical
point.   The   talk   is   mainly   devoted  to
Wess-Zumino-Witten  models  and applications of
representation   reduction   technique  to  the
construction   of  modular-invariant  partition
functions.