  We construct low energy effective Lagrangians for 3d N=4 supersymmetric
Yang-Mills theory with any gauge group. They represent supersymmetric sigma
models at hyper-Kahlerian manifolds of dimension 4r (r is the rang of the
group). In the asymptotic region, perturbatively exact explicit expression for
the metric are written. We establish the relationship of this metric with the
TAUB-NUT metric describing the perturbatively exact effective Lagrangians for
unitary groups and monopole moduli spaces: the former is obtained out of the
latter by a proper hyper-Kahlerian reduction. We describe in details the
reduction procedure for SO/Sp/G_2 gauge groups, where it can also be given a
natural interpretation in D-brane language. We conjecture that the exact
nonperturbative metrics can be obtained by a similar hyper-Kahlerian reduction
from the corresponding multidimensional Atiyah-Hitchin metrics.
