The physics programme of the NA62 experiment at the CERN SPS accelerator is organised in two phases. During the first phase (2007-2008) data were collected to study Lepton Universality with kaon decays. For my PhD thesis the same data sample is used to measure the branching ratio of the radiative K+->e+nugamma decay, which is a key ingredient to reach a precision better than 0.4% in the Lepton Universality test. The second phase (2013-2014) will measure the branching ratio of the rare K+->pi+nunubar decay with a ~10% accuracy. Within my PhD activity I am also currently in charge of a MonteCarlo simulation for a Differential Cherenkov detector that works with high rate particle beams to identify and tag charged kaons. Such detector is crucial to the success of the NA62 second phase.