A generalization of the theory of relativity is considered in which
spacetime $M_4$ is replaced by the configuration space
${\cal C}$ associated with a given physical system. In particular,
for a system of point particles we assume that its dynamical
behavior is determined by the minimal length action in ${\cal C}$.
In other words, the system is considered as a point that traces
a geodetic line in configuration space. The theory thus predicts in
general a different dynamical behavior for a many particle system
than does the ordinary theory. But in particular, for a suitable metric
of ${\cal C}$, we obtain the ordinary many particle action in the
presence of gravitational field. In general, the configuration space
can have non vanishing curvature. From the point of view of 4-dimensional
spacetime, which is a subspace of ${\cal C}$, there exist extra
forces that act on a particle, besides the ordinary gravity.
Observations suggest that the ordinary theory cannot be straightforwardly
applied to the large scale system such as galaxies, clusters of galaxies and
the universe. Instead one has to introduce the concept of dark matter and
dark energy, or alternatively, to consider suitable modifications of
the theory of gravity (MOND). We propose to explore the possibility
that general relativity, not in spacetime $M_4$, but in multidimensional
configuration space ${\cal C}$ might solve such astrophysical puzzles.
The theory can also be applied to other sorts of configuration spaces,
e.g., those associated with extended objects such as strings and branes.
This enables a deeper understanding of the geometric principle behind
the string theory, and the insight on the occurrence of the Yang-Mills
and gravitational fields.
