My current research interests are centered around several aspects of classical and quantum gauge theories, in particular, theories which are invariant under the group of diffeomorphisms, such as topological field theories, BF-like models and gravity. In the classical setting, the approaches I am most familiar with are the constrained Hamiltonian analysis, the canonical covariant methods and multisymplectic geometry, which is a fully covariant scheme and a mathematically rigorous treatment of field theories. In the quantum aspect, I have been involved in different studies of the framework known as the deformation quantization formalism, and with non-perturbative canonical quantization methods, also known as Loop Quantum Gravity (LQG). Related to this, I am very interested in the fundamental problem of making general relativity and quantum theory compatible in what is called as quantum gravity. One of the most interesting results obtained from LQG, is that the geometry behaves in a quantum way, and the spectra of geometric operators turn out to be discrete and non-commutative. These results posses very interesting questions related to the problem of recovering the commutative, smooth geometry in a certain limit. In order to address this question, we have been studying the LQG approach under the deformation quantization formalism. Under this formalism, the Dirac quantization rules are achieved by replacing the usual product of the algebra of smooth functions on the classical phase space with an associative non-commutative product, such that the resulting commutator is a deformation of the Poisson structure.