  A loop space formulation of Yang-Mills theory high-lighting the significance
of monopoles for the existence of gauge potentials is used to derive a
generalization of electric-magnetic duality to the nonabelian theory. The
result implies that the gauge symmetry is doubled from SU(N) to $SU(N) \times
\widetilde{SU}(N)$, while the physical degrees of freedom remain the same, so
that the theory can be described in terms of either the usual Yang-Mills
potential $A_\mu(x)$ or its dual $\tilde{A}_\mu(x)$. Nonabelian `electric'
charges appear as sources of $A_\mu$ but as monopoles of $\tilde{A}_\mu$, while
their `magnetic' counterparts appear as monopoles of $A_\mu$ but sources of
$\tilde{A}_\mu$. Although these results have been derived only for classical
fields, it is shown for the quantum theory that the Dirac phase factors (or
Wilson loops) constructed out of $A_\mu$ and $\tilde{A}_\mu$ satisfy the 't
Hooft commutation relations, so that his results on confinement apply. Hence
one concludes, in particular, that since colour SU(3) is confined then dual
colour $\widetilde{SU}(3)$ is broken. Such predictions can lead to many very
interesting physical consequences which are explored in a companion paper.
