  We demonstrate electric-magnetic duality in N=1 supersymmetric non-Abelian
gauge theories in four dimensions by presenting two different gauge theories
(different gauge groups and quark representations) leading to the same
non-trivial long distance physics. The quarks and gluons of one theory can be
interpreted as solitons (non-Abelian magnetic monopoles) of the elementary
fields of the other theory. The weak coupling region of one theory is mapped to
a strong coupling region of the other. When one of the theories is Higgsed by
an expectation value of a squark, the other theory is confined. Massless
glueballs, baryons and Abelian magnetic monopoles in the confining description
are the weakly coupled elementary quarks (i.e.\ solitons of the confined
quarks) in the dual Higgs description.
