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 T1/2 = (2.62 ± 0.14) × 1019 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 T1/2≥ 1.9 × 1023 yr at 90% CL, which corresponds to the effective Majorana neutrino mass limit (mv) ≤ (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.