  The properties of uniformly rotating white dwarfs (RWDs) are analyzed within
the framework of general relativity. Hartle's formalism is applied to construct
the internal and external solutions to the Einstein equations. The WD matter is
described by the relativistic Feynman-Metropolis-Teller equation of state which
generalizes the Salpeter's one by taking into account the finite size of the
nuclei, the Coulomb interactions as well as electroweak equilibrium in a
self-consistent relativistic fashion. The mass $M$, radius $R$, angular
momentum $J$, eccentricity $\epsilon$, and quadrupole moment $Q$ of RWDs are
calculated as a function of the central density $\rho_c$ and rotation angular
velocity $\Omega$. We construct the region of stability of RWDs ($J$-$M$ plane)
taking into account the mass-shedding limit, inverse $\beta$-decay instability,
and the boundary established by the turning-points of constant $J$ sequences
which separates stable from secularly unstable configurations. We found the
minimum rotation periods $\sim 0.3$, 0.5, 0.7 and 2.2 seconds and maximum
masses $\sim 1.500$, 1.474, 1.467, 1.202 $M_\odot$ for $^{4}$He, $^{12}$C,
$^{16}$O, and $^{56}$Fe WDs respectively. By using the turning-point method we
found that RWDs can indeed be axisymmetrically unstable and we give the range
of WD parameters where it occurs. We also construct constant rest-mass
evolution tracks of RWDs at fixed chemical composition and show that, by
loosing angular momentum, sub-Chandrasekhar RWDs (mass smaller than maximum
static one) can experience both spin-up and spin-down epochs depending on their
initial mass and rotation period while, super-Chandrasekhar RWDs (mass larger
than maximum static one), only spin-up.
