  As the value of the longitudinal momentum carried by partons in a
ultra-relativistic hadron becomes small, one observes a growth of their
density. When the parton density becomes close to a value of order
$1/\alpha_s$, it does not grow any longer, it saturates. These high density
effects seem to be well described by the Color Glass Condensate effective field
theory. On the experimental side, the LHC provides the best tool ever for
reaching the saturated phase of hadronic matter. For this reason saturation
physics is a very active branch of QCD during these past and coming years since
saturation theories and experimental data can be compared. I first deal with
the phenomenology of the proton-lead collisions performed in winter 2013 at the
LHC and whose data are about to be available. I compute the di-gluon production
cross-section which provides the simplest observable for finding quantitative
evidences of saturation in the kinematic range of the LHC. I also discuss the
limit of the strongly correlated final state at large transverse momenta and by
the way, generalize parton distribution to dense regime. The second main topic
is the quantum evolution of the quark and gluon spectra in nucleus-nucleus
collisions having in mind the proof of its universal character. This result is
already known for gluons and here I detail the calculation carefully. For
quarks universality has not been proved yet but I derive an intermediate
leading order to next-to leading order recursion relation which is a crucial
step for extracting the quantum evolution. Finally I briefly present an
independent work in group theory. I detail a method I used for computing traces
involving an arbitrary number of group generators, a situation often
encountered in QCD calculations.
