  The Cosmology Large Angular Scale Surveyor (CLASS) is a telescope array that
observes the cosmic microwave background over 75\% of the sky from the Atacama
Desert, Chile, at frequency bands centered near 40, 90, 150, and 220~GHz. This
paper describes the CLASS data pipeline and maps for 40~GHz observations
conducted from August 2016 to May 2022. We demonstrate how well the CLASS
survey strategy, with rapid ($\sim10\,\mathrm{Hz}$) front-end modulation,
recovers the large-scale Galactic polarization signal from the ground: the
mapping transfer function recovers $\sim75$\% of $EE$, $BB$, and $VV$ power at
$\ell=20$ and $\sim45$\% at $\ell=10$. We present linear and circular
polarization maps over 75\% of the sky. Simulations based on the data imply the
maps have a white noise level of $110\,\mathrm{\mu K\, arcmin}$ and correlated
noise component rising at low-$\ell$ as $\ell^{-2.2}$. The
transfer-function-corrected low-$\ell$ component is comparable to the white
noise at the angular knee frequencies of $\ell\approx16$ (linear polarization)
and $\ell\approx12$ (circular polarization). Finally, we present simulations of
the level at which expected sources of systematic error bias the measurements,
finding sub-percent bias for the $\Lambda\mathrm{CDM}$ $EE$ power spectra. Bias
from $E$-to-$B$ leakage due to the data reduction pipeline and polarization
angle uncertainty approaches the expected level for an $r=0.01$ $BB$ power
spectrum. Improvements to the instrument calibration and the data pipeline will
decrease this bias.
