  Classical affine Lie algebras appear e.g. as symmetries of infinite
dimensional integrable systems and are related to certain differential
equations. They are central extensions of current algebras associated to
finite-dimensional Lie algebras g. In geometric terms these current algebras
might be described as Lie algebra valued meromorphic functions on the Riemann
sphere with two possible poles. They carry a natural grading. In this talk the
generalization to higher genus compact Riemann surfaces and more poles is
reviewed. In case that the Lie algebra g is reductive (e.g. g is simple,
semi-simple, abelian, ...) a complete classification of (almost-) graded
central extensions is given. In particular, for g simple there exists a unique
non-trivial (almost-)graded extension class. The considered algebras are
related to difference equations, special functions and play a role in Conformal
Field Theory.
