  This thesis investigates low-dimensional models of nonperturbative quantum
gravity, with a special focus on Causal Dynamical Triangulations (CDT). We
define the so-called curvature profile, a new quantum gravitational observable
based on the quantum Ricci curvature. We subsequently study its coarse-graining
capabilities on a class of regular, two-dimensional polygons with isolated
curvature singularities, and we determine the curvature profile of
(1+1)-dimensional CDT with toroidal topology. Next, we focus on CDT in 2+1
dimensions, intvestigating the behavior of the two-dimensional spatial slice
geometries. We then turn our attention to matrix models, exploring a
differential reformulation of the integrals over one- and two-matrix ensembles.
Finally, we provide a hands-on introduction to computer simulations of CDT
quantum gravity.
