Locally, there are eight types of "nice", i.e., homogeneous metrics in dimension three. Besides metrics of constant curvature and their products we have also nil, sol and $SL_2(R)$ geometries, i.e., metrics which are locally isometric to the Heisenberg group, the group \emph{Sol} or the group $SL_2(R)$ of isometries of the Bolyai-Lobachevsky plane. In [6] we derived explicitly formulas for geodesic lines in the Heisenberg group \emph{Heis}. In the present note we use the same method and obtain formulas for geodesic lines in the $SL_2(R)$ and equations of geodesics in \emph{sol}-geometry, which may be solved in quadratures (with the help of elliptic functions). We also compute Cristoffel symbols and the curvature tensor and consider left-invariant Lorentz metrics.