  The 'hole argument'(the English translation of German 'Lochbetrachtung') was
formulated by Albert Einstein in 1913 in his search for a relativistic theory
of gravitation. The hole argument was deemed to be based on a trivial error of
Einstein, until 1980 when John Stachel (Talk on Einsteins Search for General
Covariance, 1912-1915 at the GRG meeting in Jena 1980) recognized its highly
non-trivial character. Since then the argument has been intensively discussed
by many physicists and philosophers of science. (See e.g., Earman & Norton
(1987), Gaul & Rovelli (1999), Stachel & Iftime(2005}, and Iftime &
Stachel(2006).)
  I shall provide here a coordinate-free formulation of the argument using the
language of categories and bundles, and generalize the argument for arbitrary
covariant and permutable theories (see Iftime & Stachel(2006). In conclusion I
shall point out a way of avoiding the hole argument, by looking at the
structure of the space of solutions of Einstein's equations on a space-time
manifold. This superspace Q(M) is defined as the orbit space of space-time
solutions on M under the action of the diffeomorphisms of M, and it plays an
important role in the study of the gravitational field and attempts to find a
theory of quantum gravity (QG).
