  Many recent researches indicate that several gravitational D-dimensional
theories suitably coupled to some matter fields (including in particular pure
gravity in D dimensions, the low energy effective actions of the bosonic string
and the bosonic sector of M-theory) would be characterized by infinite
dimensional Kac-Moody algebras G^{++} and G^{+++}. The possible existence of
these extended symmetries motivates a development of a new description of
gravitational theories based on these symmetries. The importance of Kac-Moody
algebras and the link between the G^{+++}-invariant theories and the
uncompactified space-time covariant theories are discussed.
