  We discuss a general theory of Lorentzian Kac--Moody algebras which should be
a hyperbolic analogy of the classical theories of finite-dimensional
semi-simple and affine Kac-Moody algebras. First examples of Lorentzian
Kac-Moody algebras were found by Borcherds. We consider general finiteness
results about the set of Lorentzian Kac--Moody algebras and the problem of
their classification. As an example, we give classification of Lorentzian
Kac--Moody algebras of the rank three with the symmetry group which is an
extended paramodular group. Perhaps, this is the first example when a large
class of Lorentzian Kac--Moody algebras was classified. This paper is closely
related with our papers math.AG/9810001, math.AG/0010329
