In this thesis we developed, validated and applied to data, the most advanced statistical tools to measure NG in the high resolution CMB datasets coming from the Planck satellite First Cosmology Public Release. In particular, our efforts were conveyed to the development of the so called (Komatsu-Spergel-Wandelt) KSW estimator (Komatsu et al. 2005), the Planck breeded version of the estimator used by the WMAP team, that was selected as a front-runner estimator for NG for the Planck first public release. Moreover, we developed a second estimator, the Skew-Cl (Munshi and Heavens 2010). This estimator has the advantage to estimate NG in armonic space giving rise the possibility to study possible contamination that can be present in the data. In the conclusion we will describe and discuss the results we obtained, showing not only the numbers, but focusing in particular on their robustness, achieved through an intense campaign of validation made inside the Planck collaboration, that allowed us to claim the final constraint on inflationary NG.
