  This thesis start by a review of different approaches to classical and
quantum gravity. The main theme is Lorentzian Gromov Hausdorff theory which is
an active diffeomorphism invariant theory on the space of Lorentz spaces (think
about globally hyperbolic spacetimes). It is argued why such theory might be of
significant importance for Lorentzian approaches to quantum gravity such as
causal set theory and Lorentzian dynamical triangulations
