We present ^ { 12 } CO J =1–0 and J =2–1 Swedish-ESO Submillimetre Telescope ( SEST ) observations of the barred spiral galaxy M83 ( NGC5236 ) . The size of the CO maps is 10′ \times 10′ and they cover the entire optical disk . The grid spacing is 11″ for CO ( J =1–0 ) and 11″ or 7″ for CO ( J =2–1 ) depending on the position in the galaxy . In total we have obtained spectra in 1900 and 2574 positions in the CO ( J =1–0 ) and CO ( J =2–1 ) lines , respectively . The CO emission is strongly peaked toward the nucleus , which breaks up into two separate components in the CO ( J =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° . Emission in the inter-arm regions is detected . The average CO ( J =2–1 ) / ( J =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 } M _ { \odot } . The total molecular gas mass is estimated to be 3.9 \times 10 ^ { 9 } M _ { \odot } . 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 .