  We discuss non-trivial fixed points of the renormalization group with dual
descriptions in $N=4$ gauge theories in three dimensions. This new duality acts
as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories.
Quantum effects on the Coulomb branch arise classically on the Higgs branch of
the dual theory. We present examples of dual theories whose Higgs/Coulomb
branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space
of instantons of the corresponding $ADE$ gauge group. In particular, we show
that in three dimensions small $E_8$ instantons in string theory are described
by a local quantum field theory.
