  Among eight possible geometric structures on three-dimensional manifolds less
studied from the differential geometric point of view are those modelled on the
Heisenberg group $Heis^3$. We consider the Heisenberg left-invariant metric and
use some results on Levi-Civita connection and curvature tensor to present
solutions of equations for geodesic lines in the Heisenberg group. Using
"Mathematica" software package we also present drawings of geodesic lines and
metric balls in the Heisenberg group.
