  A potentially powerful approach to quantum gravity has been developed over
the last few years under the name of Causal Dynamical Triangulations. Numerical
simulations have given very interesting results in the cases of two, three and
four spacetime dimension. The aim of this thesis is to give an introduction to
the subject (Chapter 1), and try to push the analytical understanding of these
models further. This is done by first studying (Chapter 2) the case of a
(1+1)-dimensional spacetime coupled to matter, in the form of an Ising model,
by means of high- and low-temperature expansions. And after (Chapter 3) by
studying a specific model in (2+1) dimensions, whose solution and continuum
limit are presented.
