  The NEMO-3 experiment at the Modane Underground Laboratory has investigated
the double-$\beta$ decay of $^{48}{\rm Ca}$. Using $5.25$ yr of data recorded
with a $6.99\,{\rm g}$ sample of $^{48}{\rm Ca}$, approximately $150$
double-$\beta$ decay candidate events have been selected with a
signal-to-background ratio greater than $3$. The half-life for the two-neutrino
double-$\beta$ decay of $^{48}{\rm Ca}$ has been measured to be
$T^{2\nu}_{1/2}\,=\,[6.4\, ^{+0.7}_{-0.6}{\rm (stat.)} \, ^{+1.2}_{-0.9}{\rm
(syst.)}] \times 10^{19}\,{\rm yr}$. A search for neutrinoless double-$\beta$
decay of $^{48}{\rm Ca}$ yields a null result and a corresponding lower limit
on the half-life is found to be $T^{0\nu}_{1/2} > 2.0 \times 10^{22}\,{\rm yr}$
at $90\%$ confidence level, translating into an upper limit on the effective
Majorana neutrino mass of $< m_{\beta\beta} > < 6.0 - 26$ ${\rm eV}$, with the
range reflecting different nuclear matrix element calculations. Limits are also
set on models involving Majoron emission and right-handed currents.
