Oscillations between members of flavoured, electrically neutral meson pairs and the CP violation are phenomena strictly connected with the mixing. However, CP is more general, having been observed also in the decay of charged mesons.

CP violation was first observed in the neutral K system. We see the states of definite strangeness, those of definite CP and those with definite mass and lifetime. The oscillation between the former states, the mathematical expressions and the experimental evidence.

The oscillations and CP violation in the B0 system, and the beautiful experimental results obtained at dedicated high-luminosity electron–positron colliders, the ‘beauty factories’. Beauty physics at the dedicated experiment LHCb at LHC, in particular for the B0, that is not accessible to beauty factories. Examples of CP violation in B0. The recent discovery of CP violation in the charm sector.

How the many different measurements can be put together to test the SM with the unitary triangle.

Neutrinos are the most difficult particle to study, because they interact only via weak interactions. However, they have given revolutionary surprises, and it is with neutrinos that physics beyond the SM has been discovered. In the SM, neutrino masses are rigorously zero, but experiments show that they do have a mass. In the SM, neutrino flavour eigenstates are mass eigenstates; experiments show that they are mixtures of them. Two discoveries proved this. One is neutrino oscillations, discovered in atmospheric neutrinos, the other is the adiabatic flavour conversion in matter, discovered in solar neutrinos.

These were with natural neutrinos. Several experiments have been, and are being, performed with artificial neutrinos from reactors or accelerators to measure with increasing accuracy the neutrino mixing matrix and the mass spectrum. We found that the neutrino mixing is much larger than that of the quarks. Nobody knows why.

The SM assumes neutrinos to be different from antineutrinos, but no experimental proof of it exists. Neutrinos and antineutrinos may well be the same particle, a Majorana spinor. We see how this is searched for by looking for the extremely rare double beta decay.

This chapter presents the last interaction described by the Standard Model of particle physics, i.e. the weak interaction. A historical approach is followed, trying to explain the evolution of its theoretical description from the experimental discoveries: we start from Fermi theory before introducing the charged and neutral currents. The mixing matrices both in the quark sector and in the leptonic sector are described. The phenomenon of neutrino oscillation is also detailed. The chapter concludes with a detailed discussion of CP violation.

This chapter deals with basic aspects of flavor physics in the charm sector. It isnot as detailed as other ones. Yet, it contains many fundamentals related to CP violation and mixing in the charm sector.

In this chapter we present a detailed discussion of the particle-antiparticle mixing in the SM and perform the classification of various types of CP violation. We will discuss the determination of the CKM parameters in tree-level decays and also the determination of the so-called unitarity triangle from particle-antipartcle mixing both from Band K meson systems and tree-level decays in question. In this context we will present various methods for the determination of the angles in this triangle from certain leading decays. The considered decays are subject to only small contributions from NP so that the CKM parameters can be extracted without knowledge of what happens beyond the SM. This is useful as then the results of tree-level determinations of CKM parameterscan be used to find SM predictions forparticle-antiparticle mixing observables considered already in this chapter and for rare processes considered in the next two chapters. Both particle-antiparticle mixing and rare processes are subject to potential NP contributions and could help us to identify NP through the pattern of deviations of the data for themfrom SM predictions.