  We consider the theories obtained by dimensional reduction to D=1,2,3 of 4D
supersymmetric Yang--Mills theories and calculate there the effective
low-energy lagrangia describing moduli space dynamics -- the low-dimensional
analogs of the Seiberg--Witten effective lagrangian. The effective theories
thus obtained are rather beautiful and interesting from mathematical viewpoint.
In addition, their study allows one to understand better some essential
features of 4D supersymmetric theories, in particular -- the nonrenormalisation
theorems.
