Starlight contains a wealth of information that can be used to work out fundamental stellar parameters – temperatures, masses, chemical compositions – thus revealing the nature of not just the stars themselves, but also the atoms they are made of, the planets that orbit them, and the galaxies that they live in. However, sophisticated models of stellar spectra are needed in order to compare with and thus accurately decode real observations of stars. Classical analyses are based on one-dimensional (1D) model stellar atmospheres that are assumed to satisfy local thermodynamic equilibrium (LTE). These assumptions are now known to fail for late-type stars like our Sun, whose atmospheres are inhomogeneous and dynamical as a result of their convective envelopes, and are in non-LTE conditions due to the intense radiation field being emitted. In this project, we shall construct accurate models of stellar spectra, using state-of-the-art atomic physics and 1D non-LTE, 3D LTE, and ultimately 3D non-LTE radiative transfer. These new models will be compared against observations of the Sun and other stars in our Galaxy, to provide the most accurate estimates of their fundamental parameters, and to provide fresh insight into the physics of atoms, planets, stars, and galaxies. The calculations will be carried out with the Fortran/MPI code Balder, that is developed by our group and has been tested and run at several HPC centres around the world.