  The understanding of the non-perturbative regime of YM theories remains a
challenging open problem in theoretical physics. Notably, a satisfactory
description of the confinement of gluons is not at our disposal so far. In this
thesis, the RGZ framework, designed to provide a proper quantization of YM
theories by taking into account the existence of the so-called Gribov copies is
explored. Successfully introduced in the Landau gauge, the RGZ set up does not
extend easily to different gauges. The main reason is that a clear formulation
of the analogue of the Gribov horizon in the Landau gauge is obstructed by
technical difficulties when more sophisticated gauges are chosen. Moreover, the
RGZ action breaks BRST symmetry explicitly, making the task of extracting gauge
invariant results even more difficult. The main goal of the present thesis is
precisely to provide a consistent framework to extend the RGZ action to gauges
that are connected to Landau gauge via a gauge parameter. Our main result is
the reformulation of the theory in the Landau gauge with appropriate variables
such that a non-perturbative BRST symmetry is constructed. This symmetry
corresponds to a deformation of the standard BRST symmetry by taking into
account non-perturbative effects. This opens a toolbox which allow us to
explore what would be the Gribov horizon in different gauges as linear
covariant and Curci-Ferrari gauges. Consistency with gauge independence of
physical quantities as well as the computation of the gluon propagator in these
gauges is provided. Remarkably, when lattice or functional methods results are
available, we verify very good agreement with our analytical proposal giving
support that it could provide some insights about the non-perturbative regime
of YM theories. A positivity violating gluon propagator in the infrared seems
to be a general feature of the formalism.
