  We describe the production and verification of sky maps of the five SPIRE
fields observed as part of the Herschel Multi-tiered Extragalactic Survey
(HerMES) during the Science Demonstration Phase (SDP) of the Herschel mission.
We have implemented an iterative map-making algorithm (SHIM; The SPIRE-HerMES
Iterative Mapper) to produce high fidelity maps that preserve extended diffuse
emission on the sky while exploiting the repeated observations of the same
region of the sky with many detectors in multiple scan directions to minimize
residual instrument noise. We specify here the SHIM algorithm and outline the
various tests that were performed to determine and characterize the quality of
the maps and verify that the astrometry, point source flux and power on all
relevant angular scales meets the needs of the HerMES science goals. These
include multiple jackknife tests, determination of the map transfer function
and detailed examination of the power spectra of both sky and jackknife maps.
The map transfer function is approximately unity on scales from one arcminute
to one degree. Final maps (v1.0), including multiple jackknives, as well as the
SHIM pipeline, have been used by the HerMES team for the production of SDP
papers.
