  We present weak lensing shear catalogues from the fourth data release of the
Kilo-Degree Survey, KiDS-1000, spanning 1006 square degrees of deep and
high-resolution imaging. Our `gold-sample' of galaxies, with well-calibrated
photometric redshift distributions, consists of 21 million galaxies with an
effective number density of $6.17$ galaxies per square arcminute. We quantify
the accuracy of the spatial, temporal, and flux-dependent point-spread function
(PSF) model, verifying that the model meets our requirements to induce less
than a $0.1\sigma$ change in the inferred cosmic shear constraints on the
clustering cosmological parameter $S_8 = \sigma_8\sqrt{\Omega_{\rm m}/0.3}$.
Through a series of two-point null-tests, we validate the shear estimates,
finding no evidence for significant non-lensing B-mode distortions in the data.
The PSF residuals are detected in the highest-redshift bins, originating from
object selection and/or weight bias. The amplitude is, however, shown to be
sufficiently low and within our stringent requirements. With a shear-ratio
null-test, we verify the expected redshift scaling of the galaxy-galaxy lensing
signal around luminous red galaxies. We conclude that the joint KiDS-1000 shear
and photometric redshift calibration is sufficiently robust for combined-probe
gravitational lensing and spectroscopic clustering analyses.

Cosmology and Nongalactic Astrophysics