The nature of the first stars, or Population III (Pop III) stars, in our universe remains an elusive topic in astronomy. It is part of the wider research field of Galactic archaeology that aims to understand the chemical and dynamical evolution of our Milky Way, and the field of early-universe cosmology. The lack of direct observations of these stars necessitates other indirect methods to study their properties. For example, the direct descendants of Pop III stars, so-called Population II stars, are still alive and observable. The chemical composition and kinematics of these metal-poor Pop II stars reflect the conditions of their birth environment. As such, the oldest most-metal poor stars should reflect the nucleosynthesis yields of the first stars, ejected into the interstellar medium through supernovae. In addition, Pop II stars trace the substructure of the Milky Way and its past evolution, characterised by large- and small-scale merger events.

In order to understand these aforementioned topics, we need to be able to accurately determine the chemical composition of metal-poor Pop II stars. Traditionally, one-dimensional (1D) hydrostatic simulations of stellar atmospheres together with the assumption of local thermodynamic equilibrium (LTE) are used to determine the chemical composition of stars. However, it is known that these assumptions are physically incorrect and can lead to erroneous results. More accurate methods exist that combine three-dimensional (3D) simulations coupled with modelling spectral line formation in non-local thermodynamic equilibrium (non-LTE).

The goal of this thesis is twofold: firstly, showcase the need for a comprehensive 3D non-LTE modelling approach to accurately determine the chemical composition of metal-poor stars, and secondly, provide tools and data to the scientific community to make such modelling more accessible. In Paper I, we took advantage of the latest numerical tools and atomic data to redetermine the chemical composition of the most metal-poor star known to date, SDSS J102915.14+172927.9. In Paper II, I joined a collaborative effort to update and release for the first time a public grid of 3D model atmospheres. These model atmospheres are a vital component of computing synthetic spectra in 3D non-LTE, such as done in Paper I. Lastly, in Paper III, we investigated the impact of 3D non-LTE on the formation of several strong spectral lines of ionised calcium, and how this translates into derived calcium abundances. We computed a grid of synthetic spectra in 3D non-LTE and provided corresponding abundance corrections that can be readily applied in future studies to derive accurate calcium abundances.