The NA62 project at CERN: $K^+\to\pi^+\nu\bar{\nu}$ at the SPS

There are currently three main directions in elementary particle physics. On the one hand experiments at the highest possible energies are searching for the origin of electroweak breaking and direct evidence of New Physics (NP); a second line of attack aims to study the properties of neutrinos, both of accelerator and cosmic origin, and of other astro-particle messengers. The third strategy is to explore the precision frontier looking for deviations from the Standard Model (SM) predictions in rare or forbidden processes. In this latter case, the sensitivity to NP originates from the virtual contributions that can involve all discovered and not yet discovered particles in higher order quantum loops and therefore can address, indirectly, energy scales even beyond those accessible at colliders. Some of the most interesting rare decays are those Flavour Changing Neutral Currents (FCNC) that can be predicted with small hadronic uncertainties in the SM. There arc only very few observables where there is both sensitivity to NP and a well calculable expectation within the SM. A very good example is the $K^+ \to {\pi^+} \nu \bar {\nu}$ decay which will be studied by the NA62 experiment at the CERN SPS.