with the mixing amplitudes Uej. In this case, what the experiments really measure is the quantity where is a CP phase equal to , and the sum is to be extended over all two-component Majorana neutrinos that mix with . Another consequence of neutrino mixing is the phenomenon of flavour oscillations which is the most important indirect method to search for neutrino masses. A neutrino produced as a is generally a superposition of three mass eigenstates. Along a beam (z-direction) each of them acquires a phase according to the plane-wave propagation with . Because the different mass components acquire different phases so that downstream one finds a new superposition. One distinguishes between appearance experiments where one searches for a neutrino flavour different from the one produced at the source, and disappearance experiments where a flux depletion of the originally produced flavour is looked for. In general, U is a matrix, or even larger if one speculates that new (sterile) neutrino flavours exist. A general discussion of neutrino oscillations is thus quite complicated. We limit our presentation to two-flavour mixing, keeping in mind that a definitive interpretation of experimental results may require more complicated assumptions. Taking - mixing as an example, the interaction eigenstates are expressed as
in terms of the mass eigenstates and , and in terms of the mixing angle . The probability for an original to appear as a is
where L is the distance from the source and
is the oscillation length with . Depending on the source and the detector distance, different experimental techniques are needed to cover various areas in the - -parameter space. Besides accelerator neutrino beams (Sec. ) and reactors (Sec. ), both solar (Sec. ) and atmospheric neutrinos (Sec. ) have turned out to be extremely important. They exhibit signal characteristics that can be consistently interpreted by oscillations. When the neutrino beam passes through matter, notably in the case of solar and atmospheric neutrinos, the medium modifies the vacuum dispersion relation. The neutrino refractive index depends on the flavour because normal matter contains many electrons but no mu- or tau-leptons. This flavour birefringence modifies the effective mixing angle and effective as a function of matter density. When these effects are important one speaks of matter oscillations, otherwise of vacuum oscillations. In the Sun, the neutrinos are produced near the center and thus have to pass through a density gradient before they reach the surface. In this case it can happen that the effective changes sign along the beam, leading to so-called resonant oscillations or the MSW effect. In this situation one must go beyond the simple oscillation probability Eq. (). One can obtain an almost complete flavour conversion even for small mixing angles without parameter fine tuning. The experimental activities on the neutrino physics are carried out at reactors and high energy accelerators, in underground and small scale laboratories. A large part of these activities concern topics pertaining the nuclear physics. Some experiments, such as the double beta decay and the beta decay to search for the neutrino mass, involve directly the nucleus. Some others use experimental techniques typical of the low energy physics as the study of solar neutrinos and dark matter, and the experiments at the reactors. The understanding of the neutrino physics are of fundamental interest not only in the elementary particle physics but also in nuclear physics. Therefore all activities focused to fix the open problems are of great interest for both these fields.