  We present the kinematics of the molecular gas in the barred spiral galaxy
M83 (NGC5236). The study is based on ^{12}CO(J=1--0 and 2--1) observations with
the Swedish-ESO Submillimetre Telescope (SEST). Iso-velocity maps of the entire
optical disk, 10'x10' or 13x13 kpc, are produced. They show the pattern of an
inclined, rotating disk, but also the effects of streaming motions along the
spiral arms. A dynamical mass of about 6x10^10 M_sun is estimated by fitting
the rotation curve of an exponential disk model to these data. The gas
constitutes about 13% of the disk mass. The pattern speed is determined from
the residual velocity pattern The locations of various resonances are
discussed. The molecular gas velocity dispersion is determined, and a trend of
decreasing dispersion with increasing galactocentric radius is found. A total
gas (H_2+HI+He) mass surface density map is presented, and compared to the
critical density for star formation of an isothermal gaseous disk. The critical
density is exceeded in the spiral arms, but not in the interarm regions. The
locations of Giant Molecular Associations (GMAs) and HII regions are consistent
with this scenario of dynamically induced star formation.
