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 ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ωch2=0.120±0.001, baryon density Ωbh2=0.0224±0.0001, scalar spectral index ns=0.965±0.004, and optical depth τ=0.054±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 100θ∗=1.0411±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-ΛCDM cosmology, the inferred late-Universe parameters are: Hubble constant H0=(67.4±0.5)km/s/Mpc; matter density parameter Ωm=0.315±0.007; and matter fluctuation amplitude σ8=0.811±0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be Neff=2.99±0.17, and the neutrino mass is tightly constrained to ∑mν<0.12eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the base-ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)