We give some simple examples of mirror Calabi-Yau fourfolds in Type II string
theory. These are realised as toroidal orbifolds. Motivated by the Strominger,
Yau, Zaslow argument we give explicitly the mirror transformation which maps
Type IIA/IIB on such a fourfold to Type IIA/IIB on the mirror. The mirrors are
related by the inclusion/exclusion of discrete torsion. Implicit in the result
is a confirmation of mirror symmetry to genus g in the string path integral.
Finally, by considering the relationship between M-theory and Type IIA theory,
we show how in M-theory on mirror Calabi-Yau fourfolds, mirror symmetry
exchanges the Coulomb branch with (one of the) Higgs branches of the theory.
This result is relevant to duality in N=2 supersymmetric gauge theories in
three dimensions.Comment: 16 Pages, Latex. One reference has been adde