  The Galactic Archaeology with HERMES (GALAH) survey is a large-scale stellar
spectroscopic survey of the Milky Way and designed to deliver chemical
information complementary to a large number of stars covered by the $Gaia$
mission. We present the GALAH second public data release (GALAH DR2) containing
342,682 stars. For these stars, the GALAH collaboration provides stellar
parameters and abundances for up to 23 elements to the community. Here we
present the target selection, observation, data reduction and detailed
explanation of how the spectra were analysed to estimate stellar parameters and
element abundances. For the stellar analysis, we have used a multi-step
approach. We use the physics-driven spectrum synthesis of Spectroscopy Made
Easy (SME) to derive stellar labels ($T_\mathrm{eff}$, $\log g$,
$\mathrm{[Fe/H]}$, $\mathrm{[X/Fe]}$, $v_\mathrm{mic}$, $v \sin i$, $A_{K_S}$)
for a representative training set of stars. This information is then propagated
to the whole survey with the data-driven method of $The~Cannon$. Special care
has been exercised in the spectral synthesis to only consider spectral lines
that have reliable atomic input data and are little affected by blending lines.
Departures from local thermodynamic equilibrium (LTE) are considered for
several key elements, including Li, O, Na, Mg, Al, Si, and Fe, using 1D MARCS
stellar atmosphere models. Validation tests including repeat observations, Gaia
benchmark stars, open and globular clusters, and K2 asteroseismic targets lend
confidence in our methods and results. Combining the GALAH DR2 catalogue with
the kinematic information from $Gaia$ will enable a wide range of Galactic
Archaeology studies, with unprecedented detail, dimensionality, and scope.
