We present the maps, source catalogue and number counts of the largest, most complete and unbiased extragalactic submillimetre survey ever undertaken: the 850-micron SCUBA HAlf Degree Extragalactic Survey (SHADES). Using the Submillimetre Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope (JCMT), SHADES mapped two separate regions of sky: the Subaru/XMM-Newton Deep Field (SXDF) and the Lockman Hole East (LH). These SCUBA maps cover 720 square arcmin with an RMS noise level of about 2 mJy and have uncovered >100 submillimetre galaxies. In order to ensure the utmost robustness of the resulting source catalogue, data reduction was independently carried out by four sub-groups drawn within the SHADES team, providing an unprecedented degree of reliability with respect to other SCUBA catalogues available from the literature. Individual source lists from the four groups were combined to produce a robust 120-object SHADES catalogue; an invaluable resource for follow-up campaigns aiming to study the properties of a complete and consistent sample of submillimetre galaxies. We present differential and integral source number counts of submillimetre galaxies and find that the differential counts are better fit with a broken power-law or a Schechter function than with a single power-law; the SHADES data alone significantly show that a break is required at several mJy, although the precise position of the break is not well constrained. We also find that an 850-micron survey complete down to 2 mJy would resolve 20-30 per cent of the Far-IR background into point sources. [abridged]
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