  We present cosmological constraints from a gravitational lensing mass map
covering 9400 sq. deg. reconstructed from CMB measurements made by the Atacama
Cosmology Telescope (ACT) from 2017 to 2021. In combination with BAO
measurements (from SDSS and 6dF), we obtain the amplitude of matter
fluctuations $\sigma_8 = 0.819 \pm 0.015$ at 1.8% precision,
$S_8\equiv\sigma_8({\Omega_{\rm m}}/0.3)^{0.5}=0.840\pm0.028$ and the Hubble
constant $H_0= (68.3 \pm 1.1)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$ at
1.6% precision. A joint constraint with CMB lensing measured by the Planck
satellite yields even more precise values: $\sigma_8 = 0.812 \pm 0.013$,
$S_8\equiv\sigma_8({\Omega_{\rm m}}/0.3)^{0.5}=0.831\pm0.023$ and $H_0= (68.1
\pm 1.0)\, \text{km}\,\text{s}^{-1}\,\text{Mpc}^{-1}$. These measurements agree
well with $\Lambda$CDM-model extrapolations from the CMB anisotropies measured
by Planck. To compare these constraints to those from the KiDS, DES, and HSC
galaxy surveys, we revisit those data sets with a uniform set of assumptions,
and find $S_8$ from all three surveys are lower than that from ACT+Planck
lensing by varying levels ranging from 1.7-2.1$\sigma$. These results motivate
further measurements and comparison, not just between the CMB anisotropies and
galaxy lensing, but also between CMB lensing probing $z\sim 0.5-5$ on
mostly-linear scales and galaxy lensing at $z\sim 0.5$ on smaller scales. We
combine our CMB lensing measurements with CMB anisotropies to constrain
extensions of $\Lambda$CDM, limiting the sum of the neutrino masses to $\sum
m_{\nu} < 0.12$ eV (95% c.l.), for example. Our results provide independent
confirmation that the universe is spatially flat, conforms with general
relativity, and is described remarkably well by the $\Lambda$CDM model, while
paving a promising path for neutrino physics with gravitational lensing from
upcoming ground-based CMB surveys.
