  In this PhD thesis, we introduced a new strategy to investigate the
kinematical and physical predictions of self dual Loop Quantum Gravity (LQG)
and by-passed the old problem of implementing quantum mechanically the so
called reality conditions inherent to the self dual Ashtekar's phase space.
  We first review the loop quantization of the spherically isolated horizon and
the computation of its micro-canonical entropy. Then we present the so called
gas of punctures model for the quantum horizon, discussing its results in the
canonical and grand-canonical ensembles and its limits.
  The fourth chapter is devoted to studying to what extend the loop
quantization based on the self dual variables could cure those problems. We
introduce a new strategy, based on an analytic continuation of the degeneracy
from $\gamma \in R$ to $\gamma = \pm i$. We review in details the construction
of the procedure, and present the results. At the leading term, we recover
exactly the Bekenstein-Hawking area law.
  The fifth chapter is devoted to understanding more precisely the interplay
between the status of the Immirzi parameter. In order to do this, we introduce
from a new toy model describing $2+1$ gravity which depends explicitly on the
Immirzi parameter.
  Finally, the sixth chapter is devoted to applying our procedure to the
simplest Loop Quantum Cosmology model. By first constructing the LQC dynamics
for any arbitrary spin j and then implementing our analytic continuation, we
show that our procedure preserves the key features of the LQC models, i.e. we
obtain a bouncing universe which admits the right semi classical limit after
the bounce.
