  We investigate a class of Lie algebras which we call {\it generalized
reductive Lie algebras}. These are generalizations of semi-simple, reductive,
and affine Kac-Moody Lie algebras. A generalized reductive Lie algebra which
has an irreducible root system is said to be {\it irreducible} and we note that
this class of algebras have been under intensive investigation in recent years.
They have also been called {\it extended affine Lie algebras}. The larger class
of generalized reductive Lie algebras has not been so intensively investigated.
We study them in this paper and note that one way they arise is as fixed point
subalgebras of finite order automorphisms. We show that the core modulo the
center of a generalized reductive Lie algebra is a direct sum of centerless Lie
tori. Therefore one can use the results known about the classification of
centerless Lie tori to classify the cores modulo centers of generalized
reductive Lie algebras.
