Abstract
The chemical composition of stars contain vital clues not only about the stars themselves but also about the conditions prevailing before their births. As such, stellar spectroscopy plays a key role in contemporary astrophysics and cosmology by probing cosmic, galactic, stellar and planetary evolution. In this review I will describe the theoretical foundations of quantitative stellar spectroscopy: stellar atmosphere models and spectral line formation. I will focus mainly on more recent advances in the field, in particular the advent of realistic time-dependent, 3D, (magneto-)hydrodynamical simulations of stellar surface convection and atmospheres and non-LTE radiative transfer relevant for stars like the Sun. I will also discuss some particular applications of this type of modelling which have resulted in some exciting break-throughs in our understanding and with wider implications: the solar chemical composition, the chemical signatures of planet formation imprinted in stellar abundances, the cosmological Li problem(s) and where the first stars may be residing today.
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