  Background: Direct determination of the neutrino mass through double-$\beta$
decay is at the present time one of the most important areas of experimental
and theoretical research in nuclear and particle physics. Purpose: We calculate
nuclear matrix elements for the extraction of the average neutrino mass in
neutrinoless double-$\beta$ decay. Methods: The microscopic interacting boson
model (IBM-2) is used. Results: Nuclear matrix elements in the closure
approximation are calculated for $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr,
$^{100}$Mo, $^{110}$Pd, $^{116}$Cd, $^{124}$Sn, $^{128}$Te, $^{130}$Te,
$^{148}$Nd, $^{150}$Nd, $^{154}$Sm, $^{160}$Gd, and $^{198}$Pt decay.
Conclusions: Realistic predictions for the expected half-lives in neutrinoless
double-$\beta$ decay with light and heavy neutrino exchange in terms of
neutrino masses are made and limits are set from current experiments.
