Aluminium plays a key role in studies of the chemical enrichment of the Galaxy and of globular clusters. However, strong deviations from LTE (non-LTE) are known to significantly affect the inferred abundances in giant and metal-poor stars. We present NLTE modeling of aluminium using recent and accurate atomic data, in particular utilizing new transition rates for collisions with hydrogen atoms, without the need for any astrophysically calibrated parameters. For the first time, we perform 3D NLTE modeling of aluminium lines in the solar spectrum. We also compute and make available extensive grids of abundance corrections for lines in the optical and near-infrared using one-dimensional model atmospheres, and apply grids of precomputed departure coefficients to direct line synthesis for a set of benchmark stars with accurately known stellar parameters. Our 3D NLTE modeling of the solar spectrum reproduces observed center-to-limb variations in the solar spectrum of the 7835 {AA} line as well as the mid-infrared photospheric emission line at 12.33 micron. We infer a 3D NLTE solar photospheric abundance of A(Al) = 6.43+-0.03, in exact agreement with the meteoritic abundance. We find that abundance corrections vary rapidly with stellar parameters; for the 3961 {AA} resonance line, corrections are positive and may be as large as +1 dex, while corrections for subordinate lines generally have positive sign for warm stars but negative for cool stars. Our modeling reproduces the observed line profiles of benchmark K-giants, and we find abundance corrections as large as -0.3 dex for Arcturus. Our analyses of four metal-poor benchmark stars yield consistent abundances between the 3961 {AA} resonance line and lines in the UV, optical and near-infrared regions. Finally, we discuss implications for the galactic chemical evolution of aluminium.
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