  Loop Quantum Cosmology adapts the techniques of Loop Quantum Gravity in the
quantization of homogeneous cosmological models obtained from General
Relativity by symmetry reduction. As a necessary step towards the extraction of
realistic results from Loop Quantum Cosmology, we should consider the inclusion
of inhomogeneities, which play a central role in current cosmology. The main
goal of this thesis is to progress in this direction. With this aim we have
studied a natural test bed to incorporate inhomogeneities in Loop Quantum
Cosmology: the linearly polarized Gowdy T3 model. This model can be regarded as
a homogeneous Bianchi I background filled with inhomogeneities propagating in
one direction. We have completed its quantization by means of a hybrid
approach, that combines the loop quantization of the homogeneous sector, within
the so-called improved dynamics scheme, with a Fock quantization for the
inhomogeneities. In order to perform this quantization as thorough as possible,
we have also reviewed the (improved dynamics) loop quantization of flat FRW
cosmologies, paradigmatic model in LQC, as well as that of the Bianchi I model.
We have proposed a new prescription for the Hamiltonian constraint operator of
these models, that displays nicer features than those of previous proposals. In
particular, we get simpler superselection sectors with a global and
well-understood Wheeler-DeWitt limit in the large volume regime, which serve to
improve our understanding of the physical Hilbert space of these models.
