  We present CO(1-0) and CO(2-1) Swedish-ESO Submillimetre Telescope (SEST)
observations of the barred spiral galaxy M83 (NGC5236). The maps cover the
entire optical disk. The CO emission is strongly peaked toward the nucleus,
which breaks up into two separate components in the CO(2-1) data due to the
higher spatial resolution. Emission from the bar is strong, in particular on
the leading edges of the bar. The molecular gas arms are clearly resolved and
can be traced for more than 360\degr . Emission in the inter-arm regions is
detected. The average CO CO(2-1)/CO(1-0) line ratio is 0.77. The ratio is lower
than this on the spiral arms and higher in the inter-arm regions. The arms show
regularly spaced concentrations of molecular gas, Giant Molecular Associations
(GMA's), whose masses are of the order 10^7 Msun. The total molecular gas mass
is estimated to be 3.9*10^9 Msun. This mass is comparable to the total HI mass,
but H_2 dominates in the optical disk. In the disk, H_2 and HI show very
similar distributions, including small scale clumping. We compare the molecular
gas distribution with those of other star formation tracers, such as B and
H_alpha images.
