  The continuum limit of loop quantum gravity is still an open problem. Indeed,
no proper dynamics in known to start with and we still lack the mathematical
tools to study its would-be continuum limit. In the present PhD dissertation,
we will investigate some coarse-graining methods that should become helpful in
this enterprise. We concentrate on two aspects of the theory's coarse-graining:
finding natural large scale observables on one hand and studying how the
dynamics of varying graphs could be cast onto fixed graphs on the other hand.
  To determine large scale observables, we study the case of hyperbolic
tetrahedra and their natural description in a language close to loop quantum
gravity. The surface holonomies in particular play an important role. This
highlights the structure of double spin networks, which consist in a graph and
its dual, which seems to also appear in works from Freidel et al. To solve the
problem of varying graphs, we consider and define loopy spin networks. They
encode the local curvature with loops around an effective vertex and allow to
describe different graphs by hidding them in a coarse-graining process.
Moreover, their definition gives a natural procedure for coarse-graining
allowing to relate different scales.
  Together, these two results constitute the foundation of a coarse-graining
programme for diffeomorphism invariant theories.
