  One of the biggest challenges to theoretical physics of our time is to find a
background-independent quantum theory of gravity.
  Today one encounters a profusion of different attempts at quantization, but
no fully accepted - or acceptable, theory of quantum gravity. Any such approach
requires a response to a question that lies at the heart of this problem. ``How
shall we resolve the tension between the background dependence of all
hitherto-successful quantum theories, both non-relativistic quantum mechanics
and special-relativistic quantum field theory, and the background independence
of classical general relativity?''
  The need for a background-independent quantization procedure forms the
starting point of my approach. In this paper I shall present a gauge-natural
formulation of general relativity, and provide some insights into the structure
of the space of geometries, which plays an important role in the construction
of a non-perturbative quantum gravity using a path integral approach, as well
as in string theory.
