The common understanding of proton-neutron pairing, whose fingerprints are currently investigated in N = Z nuclei, relies on Cooper pair mechanism and BCS-type models. In the present thesis we present an alternative approach which, contrary to BCS models, conserves exactly the particle number and the isospin. In this approach the ground state of N=Z nuclei is described as a condensate of alpha-like quartets built by two neutrons and two protons coupled to the total isospin T=0 and total spin J=0. The comparison with exact shell model calculations shows that the quartet condensation model (QCM) gives a very accurate description of pairing correlations in N=Z nuclei, much better than the BCS models. It is also shown that proton-neutron pairing and alpha-type condensation are important not only for N=Z nuclei but also for nuclei with excess neutrons. In the latter case the condensate of alpha-like quartets coexist with the condensate of the neutron pairs in excess relative to the N=Z isotope. Using the framework of QCM we have also studied the competition between the isovector and the isoscalar proton-neutron pairing in nuclei with N=Z. Our results indicate that the contribution of isoscalar pairing to the ground state pairing correlations is very small compared to the isovector pairing.
