  We explore the phases of N = 1 supersymmetric U(N) gauge theories with
fundamental matter that arise as deformations of N = 2 SQCD by the addition of
a superpotential for the adjoint chiral multiplet. As the parameters in the
superpotential are varied, the vacua of this theory sweep out various branches,
which in some cases have multiple semiclassical limits. In such limits, we
recover the vacua of various product gauge group theories, with flavors charged
under some group factors. We describe in detail the structure of the vacua in
both classical and quantum regimes, and develop general techniques such as an
addition and a multiplication map which relate vacua of different gauge
theories. We also consider possible indices characterizing different branches
and potential relationships with matrix models.
