In this thesis, we present a cosmological analysis of the galaxy clusters in the Planck MMF3 cosmology sample, which consists of 439 Sunyaev-Zel’dovich-detected clusters, with a cosmic microwave background (CMB) lensing calibration of the cluster masses. As demonstrated by Planck, galaxy clusters detected through their SZ signature offer a powerful way to constrain cosmological parameters such as Ωm, which parametrises the mean matter density of the Universe, and σ8, which characterises the amplitude of the matter perturbations. Determining the absolute cluster mass scale is, however, difficult, and some recent calibrations have yielded cosmological constraints in apparent tension with constraints in the ΛCDM model derived from the power spectra of the primary CMB anisotropies. In order to calibrate the absolute mass scale of the full Planck cluster sample, we measure the CMB lensing signals of 433 of its clusters (those with measured redshift) with Planck temperature data. We calibrate the bias and intrinsic scatter of our CMB lensing mass observable, the CMB lensing signal-to-noise, with mock observations from an N-body simulation. We then perform a joint likelihood analysis of the cluster counts and mass observables taking as input the CMB lensing signal-to-noise ratios, SZ signal-to-noise ratios, and redshifts. Our analysis uses a likelihood that properly accounts for selection effects in the construction of the cluster sample. We find σ8(Ωm/0.33)0.25 = 0.765±0.035, Ωm = 0.33±0.02, σ8 = 0.76±0.04, and 1−bSZ = 0.71±0.10, where the mass bias factor 1−bSZ relates cluster mass to the SZ mass that appears in the X-ray-calibrated cluster scaling relations. We find no evidence for tension with the Planck primary CMB constraints on ΛCDM model parameters.