  It is well known that cool star atmospheres depart from local thermodynamic
equilibrium (LTE). Accurate abundance determination requires taking those
effects into account, but the necessary non-LTE calculations are often lacking.
Our goal is to provide detailed estimates of NLTE effects for FGK type stars
for all spectral lines from the ultraviolet to the infrared that are
potentially useful as abundance diagnostics. The first paper in this series
focusses on the light elements Na, Mg and Al. The code PySME is used to compute
curves-of-growth for 2158 MARCS model atmospheres in a wide parameter range.
Nine abundance points are used to construct individual line curves-of-growth by
calculating the equivalent widths of 35 Na lines, 134 Mg lines, and 34 Al
lines. The lines are selected from the ultra-violet to the near infrared
wavelength range. We demonstrate the power of the new grids with LTE and NLTE
abundance analysis by means of equivalent width measurements of five benchmark
stars; the Sun, Arcturus, HD84937, HD140283 and HD122563. For Na, the NLTE
abundances are lower than in LTE and show markedly reduced line-to-line scatter
in the metal-poor stars. For Mg, we confirm previous reports of a significant
0.25 dex LTE ionization imbalance in metal-poor stars that is only slightly
improved in NLTE (0.18 dex). LTE abundances based on Mg II lines agree better
with models of Galactic chemical evolution. For Al, NLTE calculations strongly
reduce a 0.6 dex ionization imbalance seen in LTE for the metal-poor stars. The
abundance corrections presented in this work are in good agreement with
previous studies for the subset of lines that overlap, except for strongly
saturated lines.
