  In this chapter we review the recent results on the equilibrium
configurations of static and uniformly rotating neutron stars within the Hartle
formalism. We start from the Einstein-Maxwell-Thomas-Fermi equations formulated
and extended by Belvedere et al. (2012, 2014). We demonstrate how to conduct
numerical integration of these equations for different central densities ${\it
\rho}_c$ and angular velocities $\Omega$ and compute the static $M^{stat}$ and
rotating $M^{rot}$ masses, polar $R_p$ and equatorial $R_{\rm eq}$ radii,
eccentricity $\epsilon$, moment of inertia $I$, angular momentum $J$, as well
as the quadrupole moment $Q$ of the rotating configurations. In order to
fulfill the stability criteria of rotating neutron stars we take into
considerations the Keplerian mass-shedding limit and the axisymmetric secular
instability. Furthermore, we construct the novel mass-radius relations,
calculate the maximum mass and minimum rotation periods (maximum frequencies)
of neutron stars. Eventually, we compare and contrast our results for the
globally and locally neutron star models.
