  In order to study the ISM and the interplay between the atomic and molecular
components in a low-metallicity environment, we present a complete high angular
and spectral resolution map and data cube of the 12CO(2-1) emission from the
Local Group galaxy M33. Its metallicity is roughly half-solar, such that we can
compare its ISM with that of the Milky Way with the main changes being the
metallicity and the gas mass fraction. The data have a 12" angular resolution
(50pc) with a spectral resolution of 2.6 km/s and a mean noise level of 20 mK
per channel in antenna temperature. A radial cut along the major axis was also
observed in the 12CO(1-0) line. The CO data cube and integrated intensity map
are optimal when using HI data to define the baseline window and the velocities
over which the CO emission is integrated. Great care was taken when building
these maps, testing different windowing and baseline options and investigating
the effect of error beam pickup. The total CO(2-1) luminosity is 2.8e7 K km/s
pc2, following the spiral arms in the inner disk. There is no clear variation
in the CO(2-1/1-0) intensity ratio with radius and the average value is roughly
0.8. The total molecular gas mass is estimated, using a N(H2)/Ico(1-0)=4e20
cm-2/(K km/s) conversion factor, to be 3.1e8 Msol. The CO spectra in the cube
were shifted to zero velocity by subtracting the velocity of the HI peak from
the CO spectra. Hence, the velocity dispersion between the atomic and molecular
components is extremely low, independently justifying the use of the HI line in
building our maps. Stacking the spectra in concentric rings shows that the CO
linewidth and possibly the CO-HI velocity dispersion decrease in the outer
disk. Using the CO(2-1) emission to trace the molecular gas, the probability
distribution function of the H2 column density shows an excess at high column
density above a log normal distribution.
