The GALAH+ Survey: Third Data Release
  The ensemble of chemical element abundance measurements for stars, along with
precision distances and orbit properties, provides high-dimensional data to
study the evolution of the Milky Way. With this third data release of the
Galactic Archaeology with HERMES (GALAH) survey, we publish 678 423 spectra for
588 571 mostly nearby stars (81.2% of stars are within <2 kpc), observed with
the HERMES spectrograph at the Anglo-Australian Telescope. This release
(hereafter GALAH+ DR3) includes all observations from GALAH Phase 1 (bright,
main, and faint survey, 70%), K2-HERMES (17%), TESS-HERMES (5%), and a subset
of ancillary observations (8%) including the bulge and >75 stellar clusters. We
derive stellar parameters $T_\text{eff}$, $\log g$, [Fe/H], $v_\text{mic}$,
$v_\text{broad}$ & $v_\text{rad}$ using our modified version of the spectrum
synthesis code Spectroscopy Made Easy (SME) and 1D MARCS model atmospheres. We
break spectroscopic degeneracies in our spectrum analysis with astrometry from
$Gaia$ DR2 and photometry from 2MASS. We report abundance ratios [X/Fe] for 30
different elements (11 of which are based on non-LTE computations) covering
five nucleosynthetic pathways. We describe validations for accuracy and
precision, flagging of peculiar stars/measurements and recommendations for
using our results. Our catalogue comprises 65% dwarfs, 34% giants, and 1%
other/unclassified stars. Based on unflagged chemical composition and age, we
find 62% young low-$\alpha$, 9% young high-$\alpha$, 27% old high-$\alpha$, and
2% stars with $\mathrm{[Fe/H]} \leq -1$. Based on kinematics, 4% are halo
stars. Several Value-Added-Catalogues, including stellar ages and dynamics,
updated after $Gaia$ eDR3, accompany this release and allow chrono-chemodynamic
analyses, as we showcase.
