We present sensitive 850 \mu m imaging of the COSMOS field using 640 hr of new and archival observations taken with SCUBA–2 at the East Asian Observatory ’ s James Clerk Maxwell Telescope . The SCUBA–2 COSMOS survey ( S2COSMOS ) achieves a median noise level of \sigma _ { 850 \mu { \mathrm { m } } } = 1.2 mJy beam ^ { -1 } over an area of 1.6 sq . degree ( main ; Hubble Space Telescope / Advanced Camera for Surveys footprint ) , and \sigma _ { 850 \mu { \mathrm { m } } } = 1.7 mJy beam ^ { -1 } over an additional 1 sq . degree of supplementary ( supp ) coverage . We present a catalogue of 1020 and 127 sources detected at a significance level of > 4 \sigma and > 4.3 \sigma in the main and supp regions , respectively , corresponding to a uniform 2 \% false–detection rate . We construct the single–dish 850 \mu m number counts at S _ { 850 } > 2 mJy and show that these S2COSMOS counts are in agreement with previous single-dish surveys , demonstrating that degree–scale fields are sufficient to overcome the effects of cosmic variance in the S _ { 850 } = 2–10 mJy population . To investigate the properties of the galaxies identified by S2COSMOS sources we measure the surface density of near-infrared–selected galaxies around their positions and identify an average excess of 2.0 \pm 0.2 galaxies within a 13 ^ { \prime \prime } radius ( \sim 100 kpc at z \sim 2 ) . The bulk of these galaxies represent near–infrared-selected SMGs and / or spatially–correlated sources and lie at a median photometric redshift of z = 2.0 \pm 0.1 . Finally , we perform a stacking analysis at sub–millimeter and far–infrared wavelengths of stellar–mass-selected galaxies ( M _ { \star } = 10 ^ { 10 } –10 ^ { 12 } \mathrel { M _ { \odot } } ) from z = 0–4 , obtaining high-significance detections at 850 \mu m in all subsets ( signal–to–noise ratio , SNR = 4–30 ) , and investigate the relation between far–infrared luminosity , stellar mass , and the peak wavelength of the dust SED . The publication of this survey adds a new deep , uniform sub–millimeter layer to the wavelength coverage of this well–studied COSMOS field .