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We present cosmological constraints from a cosmic shear analysis of thefourth data release of the Kilo-Degree Survey (KiDS-1000), doubling the surveyarea with nine-band optical and near-infrared photometry with respect toprevious KiDS analyses. Adopting a spatially flat $\Lambda$CDM model, we find$S_8 = \sigma_8 (\Omega_{\rm m}/0.3)^{0.5} = 0.759^{+0.024}_{-0.021}$ for ourfiducial analysis, which is in $3\sigma$ tension with the prediction of thePlanck Legacy analysis of the cosmic microwave background. We compare ourfiducial COSEBIs (Complete Orthogonal Sets of E/B-Integrals) analysis withcomplementary analyses of the two-point shear correlation function and bandpower spectra, finding results to be in excellent agreement. We investigate thesensitivity of all three statistics to a number of measurement, astrophysical,and modelling systematics, finding our $S_8$ constraints to be robust anddominated by statistical errors. Our cosmological analysis of differentdivisions of the data pass the Bayesian internal consistency tests, with theexception of the second tomographic bin. As this bin encompasses low redshiftgalaxies, carrying insignificant levels of cosmological information, we findthat our results are unchanged by the inclusion or exclusion of this sample.

KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics