  We study the moduli space of vacua of four dimensional N=1 and N=2
supersymmetric gauge theories with the gauge groups $Sp(2 N_c)$, $SO(2 N_c)$
and $SO(2 N_c +1)$ using the M theory fivebrane. Higgs branches of the N=2
supersymmetric gauge theories are interpreted in terms of the M theory
fivebrane and the type IIA $s$-rule is realized in it. In particular we
construct the fivebrane configuration which corresponds to a special Higgs
branch root. This root is analogous to the baryonic branch root in the
$SU(N_c)$ theory which remains as a vacuum after the adjoint mass perturbation
to break N=2 to N=1. Furthermore we obtain the monopole condensations and the
meson vacuum expectation values in the confining phase of N=1 supersymmetric
gauge theories using the fivebrane technique. These are in complete agreement
with the field theory results for the vacua in the phase with a single confined
photon.
