Theoretical study of important bulk properties of nuclei far from stability such us the nuclear skin and its correlation with the density dependence of the symmetry energy in uniform matter is reviewed. The formation of neutron skin and its evolution with an increase of the neutron number is investigated on the basis of a self-consistent deformed mean-field Hartree - Fock method using density-dependent Skyrme force sand pairing correlations in BCS approach. We study isotopic chains of Ni, Kr, and Sn nuclei and consider all the experimentally observed isotopes from neutron-deficien to neutron-rich ones. Various definition of the neutron skin thickness based on the differences between neutron and proton radii as well as on comparison of the tail soft he neutron and proton density distributions have been tested. The effects of deformation on the neutron skins in even-even deformed nuclei are discussed on the example of Kr isotopes. The symmetry energy, the neutron pressure and the asymmetric compressibility of spherical Ni, Sn, and Pb and deformed Kr and Sm neutron-rich even-even nuclei are calculated within the coherent density fluctuation model using the symmetry energy as a function of density within the Brueckner energy-density functional. The correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated for isotopic chains of these nuclei. The mass dependence of the nuclear symmetry energy and the neutron skin thickness are also studied together with the role of the neutron-proton asymmetry. The studied correlations reveal a smoother behavior in the case of spherical nuclei than for deformed ones. We also note that the neutron skin thickness obtained for <^>208Pb with SLy4 force is found to be in a good agreement with the recent data. In addition, we analyse the existence of peculiarities of the studied quantities in Ni and Sn isotopic chains that are not present in the Pb chain.

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