  Using data from the NEMO-3 experiment, we have measured the two-neutrino
double beta decay ($2\nu\beta\beta$) half-life of $^{82}$Se as $T_{1/2}^{2\nu}
= \left[ 9.39 \pm 0.17\,\left(\mbox{stat}\right) \pm
0.58\,\left(\mbox{syst}\right)\right] \times 10^{19}$ y under the single-state
dominance hypothesis for this nuclear transition. The corresponding nuclear
matrix element is $\left|M^{2\nu}\right| = 0.0498 \pm 0.0016$. In addition, a
search for neutrinoless double beta decay ($0\nu\beta\beta$) using 0.93 kg of
$^{82}$Se observed for a total of 5.25 y has been conducted and no evidence for
a signal has been found. The resulting half-life limit of $T_{1/2}^{0\nu} > 2.5
\times 10^{23} \,\mbox{y} \,(90\%\,\mbox{C.L.})$ for the light neutrino
exchange mechanism leads to a constraint on the effective Majorana neutrino
mass of $\langle m_{\nu} \rangle < \left(1.2 - 3.0\right) \,\mbox{eV}$, where
the range reflects $0\nu\beta\beta$ nuclear matrix element values from
different calculations. Furthermore, constraints on lepton number violating
parameters for other $0\nu\beta\beta$ mechanisms, such as right-handed
currents, majoron emission and R-parity violating supersymmetry modes have been
set.
