  We present and characterise the galaxy shape catalogue from the first 3 years
of Dark Energy Survey (DES) observations, over an effective area of ~4143
deg$^2$ of the southern sky. We describe our data analysis process and our
self-calibrating shear measurement pipeline METACALIBRATION, which builds and
improves upon the pipeline used in the DES Year 1 analysis in several aspects.
The DES Year 3 weak-lensing shape catalogue consists of 100,204,026 galaxies,
measured in the $riz$ bands, resulting in a weighted source number density of
$n_{\rm eff} = 5.59$ gal/arcmin$ ^{2}$ and corresponding shape noise $\sigma_e
= 0.261$. We perform a battery of internal null tests on the catalogue,
including tests on systematics related to the point-spread function (PSF)
modelling, spurious catalogue B-mode signals, catalogue contamination, and
galaxy properties.
