We study two-dimensional N = (4, 4) supersymmetric gauge theories with various gauge groups and various hypermultiplets in the fundamental as well as bi-fundamental and adjoint representations. They have m irror theories which become equivalent to them at strong coupling. The theory with one fundamental and one adjoint has a Higgs branch which is parametrized by the adjoint matter. We also consider theories which involve an orientifold plane. The brane realization of the Matrix theory formulation of NS 5-branes in Type II string theories is also considered.