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 2016 August to 2022 May. We demonstrate how well the CLASS survey strategy, with rapid (similar to 10 Hz) front-end modulation, recovers the large-scale Galactic polarization signal from the ground: the mapping transfer function recovers similar to 67% (85%) of EE and BB (VV) power at l = 20 and similar to 35% (47%) at l = 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 mu Karcmin and correlated noise component rising at low-l as l -2.4. The transfer-function-corrected low-l component is comparable to the white noise at the angular knee frequencies of l approximate to 18 (linear polarization) and l approximate to 12 (circular polarization). Finally, we present simulations of the level at which expected sources of systematic error bias the measurements, finding subpercent bias for the Lambda cold dark matter 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.