The velocity structure of the CO line profiles of the Mon R2 molecular cloud is studied for the combined effects of rotation and collapse motions. The CO line broadening shows that the collapse velocity (km s/sup -1/) is related to radial distance (pc) by V (r) =4.7r/sup -1/2/, if one assumes pure collapse, i.e., no turbulence. The numerical constant is in reality much less since turbulence probably makes a substantial contribution. The cloud rotates about a NW-SE axis with a projected angular velocity of 0.4 km s/sup -1/ pc/sup -1/. The rotation is a minor effect compared to the collapse. Free-fall collapse, along the rotational axis, can be observed as spatially extended high-velocity CO emission on the SE side and low-velocity emission on the opposite NW side of the dense core of the cloud. The comparison of the self-reversed CO and /sup 13/CO line profiles allows the sense of the large velocity gradient flow to be determined. This shows that the cloud is collapsing, not expanding. A comparison of CO, 6 cm and 2 mm H/sub 2/CO, and recombination line profiles also shows that a self-consistent collapse model can be constructed with one continuum source, a compact H II region, more » located on the far side of the dense molecular cloud. A second larger H II region may lie in front of the dense core.A survey of the cloud at 2..mu..m detected five sources; two sources located near the dense molecular core, including the brightest, have large infrared color indices, indicating A/sub v/approx.40 mag toward the center of the cloud. The dense nature of the core is confirmed by detection of the 3..mu..m ice feature with tau/sub ice/ approximately 1 toward the brightest infrared source. A comparison of the A/sub v/ toward all the infrared sources, with the CO column densities, indicates that only 12% of the carbon is found in CO molecules. « less