  We present a measurement of the Hubble constant ($H_{0}$) and other
cosmological parameters from a joint analysis of six gravitationally lensed
quasars with measured time delays. All lenses except the first are analyzed
blindly with respect to the cosmological parameters. In a flat $\Lambda$CDM
cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}$, a 2.4% precision measurement,
in agreement with local measurements of $H_{0}$ from type Ia supernovae
calibrated by the distance ladder, but in $3.1\sigma$ tension with $Planck$
observations of the cosmic microwave background (CMB). This method is
completely independent of both the supernovae and CMB analyses. A combination
of time-delay cosmography and the distance ladder results is in $5.3\sigma$
tension with $Planck$ CMB determinations of $H_{0}$ in flat $\Lambda$CDM. We
compute Bayes factors to verify that all lenses give statistically consistent
results, showing that we are not underestimating our uncertainties and are able
to control our systematics. We explore extensions to flat $\Lambda$CDM using
constraints from time-delay cosmography alone, as well as combinations with
other cosmological probes, including CMB observations from $Planck$, baryon
acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves
the precision of the other probes, demonstrating the strong complementarity.
Allowing for spatial curvature does not resolve the tension with $Planck$.
Using the distance constraints from time-delay cosmography to anchor the type
Ia supernova distance scale, we reduce the sensitivity of our $H_0$ inference
to cosmological model assumptions. For six different cosmological models, our
combined inference on $H_{0}$ ranges from
$\sim73$-$78~\mathrm{km~s^{-1}~Mpc^{-1}}$, which is consistent with the local
distance ladder constraints.
