  The Herschel Multi-tiered Extragalactic Survey, HerMES, is a legacy program
designed to map a set of nested fields totalling ~380 deg^2. Fields range in
size from 0.01 to ~20 deg^2, using Herschel-SPIRE (at 250, 350 and 500 \mu m),
and Herschel-PACS (at 100 and 160 \mu m), with an additional wider component of
270 deg^2 with SPIRE alone. These bands cover the peak of the redshifted
thermal spectral energy distribution from interstellar dust and thus capture
the re-processed optical and ultra-violet radiation from star formation that
has been absorbed by dust, and are critical for forming a complete
multi-wavelength understanding of galaxy formation and evolution.
  The survey will detect of order 100,000 galaxies at 5\sigma in some of the
best studied fields in the sky. Additionally, HerMES is closely coordinated
with the PACS Evolutionary Probe survey. Making maximum use of the full
spectrum of ancillary data, from radio to X-ray wavelengths, it is designed to:
facilitate redshift determination; rapidly identify unusual objects; and
understand the relationships between thermal emission from dust and other
processes. Scientific questions HerMES will be used to answer include: the
total infrared emission of galaxies; the evolution of the luminosity function;
the clustering properties of dusty galaxies; and the properties of populations
of galaxies which lie below the confusion limit through lensing and statistical
techniques.
  This paper defines the survey observations and data products, outlines the
primary scientific goals of the HerMES team, and reviews some of the early
results.
