  We analyze M theory fivebrane in order to study the moduli space of vacua of
N=1 supersymmetric $Sp(N_c)$ gauge theories with $N_f$ flavors in four
dimensions. We show how the N=2 Higgs branch can be encoded in M theory by
studying the orientifold which plays a crucial role in our work. When all the
quark masses are the same, the surface of the M theory spacetime representing a
nontrivial ${\bf S^1}$ bundle over ${\bf R^3}$ develops $A_{N_f-1}$ type
singularities at two points where D6 branes are located. Furthermore, by
turning off the masses, two singular points on the surface collide and produce
$A_{2N_f-1}$ type singularity. The sum of the multiplicities of rational curves
on the resolved surface gives the dimension of N=2 Higgs branch which agrees
with the counting from the brane configuration picture of type IIA string
theory. By rotating M theory fivebranes we get the strongly coupled dynamics of
N=1 theory and describe the vacuum expectation values of the meson field
parameterizing Higgs branch which are in complete agreement with the field
theory results. Finally, we take the limit where the mass of adjoint chiral
multiplet goes to infinity and compare with field theory results. For massive
case, we comment on some relations with recent work which deals with N=1
duality in the context of M theory.
