The NEMO 3 detector is mainly devoted to the search for the neutrinoless double beta decay (0νββ). The detector is located in the Fréjus underground laboratory, where it operates since February 2003. The detector contains several isotopes, the most abundant are ¹⁰⁰Mo (~7 kg) and ⁸²Se (~1 kg). Up to now no evidence for 0νββ decay has been observed. The corresponding limits at 90% C.L. for the half-life are T_1/2^0ν > 5.8 × 10²³ years for ¹⁰⁰Mo and T_1/2^0ν > 2.1 × 10²³ years for ⁸²Se. The half-lives of the two-neutrino double-beta decay (2νββ) for ¹⁰⁰Mo, ⁸²Se, ¹¹⁶Cd, ¹⁵⁰Nd, ⁹⁶Zr and ⁴⁸Ca are also presented in this paper.