We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter $Lambda$CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted base $Lambda$CDM in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density $Omega_c h^2 = 0.120pm 0.001$, baryon density $Omega_b h^2 = 0.0224pm 0.0001$, scalar spectral index $n_s = 0.965pm 0.004$, and optical depth $tau = 0.054pm 0.007$ (in this abstract we quote $68,%$ confidence regions on measured parameters and $95,%$ on upper limits). The angular acoustic scale is measured to $0.03,%$ precision, with $100theta_*=1.0411pm 0.0003$. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-$Lambda$CDM cosmology, the inferred late-Universe parameters are: Hubble constant $H_0 = (67.4pm 0.5)$km/s/Mpc; matter density parameter $Omega_m = 0.315pm 0.007$; and matter fluctuation amplitude $sigma_8 = 0.811pm 0.006$. We find no compelling evidence for extensions to the base-$Lambda$CDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be $N_{rm eff} = 2.99pm 0.17$, and the neutrino mass is tightly constrained to $sum m_ u< 0.12$eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -$Lambda$CDM at over $2,sigma$, which pulls some parameters that affect the lensing amplitude away from the base-$Lambda$CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)
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