  Emission at far-infrared wavelengths makes up a significant fraction of the
total light detected from galaxies over the age of Universe. Herschel provides
an opportunity for studying galaxies at the peak wavelength of their emission.
Our aim is to provide a benchmark for models of galaxy population evolution and
to test pre-existing models of galaxies. With the Herschel Multi-tiered
Extra-galactic survey, HerMES, we have observed a number of fields of different
areas and sensitivity using the SPIRE instrument on Herschel. We have
determined the number counts of galaxies down to ~20 mJy. Our constraints from
directly counting galaxies are consistent with, though more precise than,
estimates from the BLAST fluctuation analysis. We have found a steep rise in
the Euclidean normalised counts at <100 mJy. We have directly resolved 15% of
the infrared extra-galactic background at the wavelength near where it peaks.
