We present a far-IR survey of the entire Mon R2 GMC with $Herschel-SPIRE$ cross-calibrated with $Planck-HFI$ data. We fit the SEDs of each pixel with a greybody function and an optimal beta value of 1.8. We find that mid-range column densities obtained from far-IR dust emission and near-IR extinction are consistent. For the entire GMC, we find that the column density histogram, or N-PDF, is lognormal below $sim$10$^{21}$ cm$^{-2}$. Above this value, the distribution takes a power law form with an index of -2.16. We analyze the gas geometry, N-PDF shape, and YSO content of a selection of subregions in the cloud. We find no regions with pure lognormal N-PDFs. The regions with a combination of lognormal and one power law N-PDF have a YSO cluster and a corresponding centrally concentrated gas clump. The regions with a combination of lognormal and two power law N-PDF have significant numbers of typically younger YSOs but no prominent YSO cluster. These regions are composed of an aggregate of closely spaced gas filaments with no concentrated dense gas clump. We find that for our fixed scale regions, the YSO count roughly correlates with the N-PDF power law index. The correlation appears steeper for single power law regions relative to two power law regions with a high column density cut-off, as a greater dense gas mass fraction is achieved in the former. A stronger correlation is found between embedded YSO count and the dense gas mass among our regions.
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