  We present a lattice formulation which gives super Yang-Mills theories in any
dimensions with simple supersymmetry as well as extended supersymmetry in the
continuum limit without fine-tuning. We first formulate super Yang-Mills
theories with simple supersymmetry in 3,4,6,10 dimensions, incorporating the
gluino on the lattice using the overlap formalism. In 4D, exact chiral symmetry
forbids gluino mass, which ensures that the continuum limit is supersymmetric
without fine-tuning. In 3D, exact parity invariance plays the same role. 6D and
10D thories being anomalous, we formulate them as anomalous chiral gauge
theories as they are. Dimensional reduction within lattice formulation is then
applied to the theories in 3,4,6 and 10D to obtain super Yang-Mills theories in
arbitrary dimensions with either simple or extended supersymmetry.
