The Herschel Multi-tiered Extragalactic Survey (HerMES) is a legacy programme designed to map a set of nested fields totalling ˜380 deg2. Fields range in size from 0.01 to ˜20 deg2, using the Herschel-Spectral and Photometric Imaging Receiver (SPIRE) (at 250, 350 and 500 μm) and the Herschel-Photodetector Array Camera and Spectrometer (PACS) (at 100 and 160 μm), with an additional wider component of 270 deg2 with SPIRE alone. These bands cover the peak of the redshifted thermal spectral energy distribution from interstellar dust and thus capture the reprocessed optical and ultraviolet radiation from star formation that has been absorbed by dust, and are critical for forming a complete multiwavelength understanding of galaxy formation and evolution. The survey will detect of the order of 100 000 galaxies at 5σ 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. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.