The basic goal of the study of the geometry of Lie groups with a
left invariant metric is to describe the geometry of the group in terms of
 the associated metric Lie algebra, as first introduced by Milnor in 1976.
 Beginning with a brief introduction to this method, we will describe the
 geodesic properties of 2-step nilpotent Lie groups. In particular, we are
 interested in a class of 2-step nilpotent Lie groups which are constructed
from representations of compact semisimple Lie groups.