  The development of a modern and more realistic nuclear energy density
functional (EDF) for accurate predictions of properties of nuclei is the
subject of enhanced activity, since it is very important for the study of
properties of nuclear matter (NM), giant resonances and, in particular, of
properties of rare nuclei with unusual neutron-to-proton ratios. Here, we
provide a short review of the current status of the nuclear EDF and the
theoretical results obtained for properties of nuclei and nuclear matter. We
will first describe a method for determining the parameters of the EDF,
associated with the Skyrme type effective interaction, by carrying out a
Hartree-Fock based fit to extensive set of data of ground state properties and
constraints. We will then describe the fully self-consistent Hartree-Fock based
random-phase-approximation theory for calculating the strength functions S(E)
and centroid energies E_CEN of giant resonances and provide results for E_CEN
of isoscalar and isovector giant resonances of multipolarities L=0-3 for a wide
range of spherical nuclei, using 33 EDFs associated with standard form of the
Skyrme type interactions, commonly employed in the literature. We investigate
the sensitivities E_CEN of the giant resonances to bulk properties of NM and
determine constraints on NM properties, such as the incompressibility
coefficient and effective mass, by comparing with experimental data on E_CEN of
giant resonances.
