  Gravity theory based on current algebra is formulated. The gauge principle
rather than the general covariance combined with the equivalence principle
plays the pivotal role in the formalism, and the latter principles are derived
as a consequence of the theory. In this approach, it turns out that gauging the
Poincar\'e algebra is not appropriate but gauging the $SO(N,M)$ algebra gives a
consistent theory. This makes it possible to have Anti-de Sitter and de Sitter
space-time by adopting a relation between the spin connection and the tetrad
field. The Einstein equation is a part of our basic equation for gravity which
is written in terms of the spin connection. When this formalism is applied to
the $E(11)$ algebra in which the three-form antisymmetric tensor is a part of
gravity multiplet, we have a current algebra gravity theory based on M-theory
to be applied to cosmology in its classical limit. Without introducing any
other ad-hoc field, we can obtain accelerating universe in the manner of the
"inflating" universe at its early stage.
