Constraints on primordial gravitational waves from the large scales CMB data

This thesis focuses on the development of analysis tools of the primordial B modes of the Cosmic Microwave Background (CMB). Our goal is to extract the amplitude of the primordial gravitational waves produced during the inflationary period.Specifically, we are interested in the large angular scales, for which the primary B modes signal is expected to be dominant. Since these scales are particularly contaminated by polarised galactic emissions, we have studied and developed approaches to reduce those contaminations and to characterise their residuals. Those methods are applicable to satellite missions such as Planck or LiteBIRD.In order to estimate the B modes amplitude, we developed and characterised a CMB anisotropies power spectrum estimator. The algorithm is pixels-based and allows to cross-correlate maps measured by different detectors. The method is optimal and minimises the E-to-B variance leakage.We applied the cleaning and spectrum estimation approaches to the polarisation data and simulation maps publicly provided by Planck. The constraints that we deduce are in agreement with past analysis. Ultimately, we derive an upper limit on the primordial gravitational waves amplitude.