  The NEMO-3 experiment measured the half-life of the $2\nu\beta\beta$ decay
and searched for the $0\nu\beta\beta$ decay of $^{116}$Cd. Using $410$ g of
$^{116}$Cd installed in the detector with an exposure of $5.26$ y,
($4968\pm74$) events corresponding to the $2\nu\beta\beta$ decay of $^{116}$Cd
to the ground state of $^{116}$Sn have been observed with a signal to
background ratio of about $12$. The half-life of the $2\nu\beta\beta$ decay has
been measured to be $
T_{1/2}^{2\nu}=[2.74\pm0.04\mbox{(stat.)}\pm0.18\mbox{(syst.)}]\times10^{19}$
y. No events have been observed above the expected background while searching
for $0\nu\beta\beta$ decay. The corresponding limit on the half-life is
determined to be $T_{1/2}^{0\nu} \ge 1.0 \times 10^{23}$ y at the $90$ % C.L.
which corresponds to an upper limit on the effective Majorana neutrino mass of
$\langle m_{\nu} \rangle \le 1.4-2.5$ eV depending on the nuclear matrix
elements considered. Limits on other mechanisms generating $0\nu\beta\beta$
decay such as the exchange of R-parity violating supersymmetric particles,
right-handed currents and majoron emission are also obtained.
