  To study the properties of the interstellar medium in the prototypical
merging system of the Antennae galaxies (NGC 4038 and NGC 4039), we have
obtained CO(1-0), (2-1) and (3-2) line maps, as well as a map of the 870 micron
continuum emission. Our results are analysed in conjunction with data from
X-ray to radio wavelengths. In order to distinguish between exact coincidence
and merely close correspondence of emission features, we compare the
morphological structure of the different emission components at the highest
available angular resolution. To constrain the physical state of the molecular
gas, we apply models of photon dominated regions (PDRs) that allow us to fit CO
and [CII] data, as well as other indicators of widespread PDRs in the Antennae
system, particularly within the super giant molecular cloud (SGMC) complexes of
the interaction region (IAR) between the two galaxies. The modeled clouds have
cores with moderately high gas densities up to 4 10^4 / cm^3 and rather low
kinetic temperatures <=25K). At present, all these clouds, including those near
the galactic nuclei, show no signs of intense starburst activity. Thermal radio
or mid-infrared emission are all observed to peak slightly offset from the
molecular peaks. The total molecular gas mass of the Antennae system adds up to
\~10^10 M_sun. In the vicinity of each galactic nucleus, the moleculargas mass,
1-2 10^9 M_sun, exceeds that of the Galactic centre region by a factorof almost
100. Furthermore, the gas does not seem to deviate much from the N_{H_2}/I_CO
ratio typical of the disk of our Galaxy rather than our Galactic centre.
