  The Aurora experiment to investigate double beta decay of $^{116}$Cd with the
help of 1.162 kg cadmium tungstate crystal scintillators enriched in $^{116}$Cd
to 82\% is in progress at the Gran Sasso Underground Laboratory. The half-life
of $^{116}$Cd relatively to the two neutrino double beta decay is measured with
the highest up-to-date accuracy $T_{1/2}=(2.62\pm0.14)\times10^{19}$ yr. The
sensitivity of the experiment to the neutrinoless double beta decay of
$^{116}$Cd to the ground state of $^{116}$Sn is estimated as $T_{1/2} \geq
1.9\times10^{23}$ yr at 90\% CL, which corresponds to the effective Majorana
neutrino mass limit $\langle m_{\nu}\rangle \leq (1.2-1.8)$ eV. New limits are
obtained for the double beta decay of $^{116}$Cd to the excited levels of
$^{116}$Sn, and for the neutrinoless double beta decay with emission of
majorons.
