Inorganic metal halide perovskites are promising materials for future efficient and low-cost solar cells. The band gap of these materials depends on the composition and one of the most interesting candidates is cesium lead iodide that combines good electronic properties (e.g. band gap of 1.7 eV) with improved stability. The drawback is that lead is toxic, and, hence, it is desirable to replace it with an element like tin. In this project, we will investigate the influence of this substitution on the electronic structure. The band gap is expected to reduce, and, similarly to the lead-based materials, various phase transitions occur as a function of temperature. While experiments show a weak variation of the band gap across the phase transitions, ab initio calculations predict a gap variation as large as 0.5 eV. The difference is expected to originate from thermal fluctuations (not taken into account in standard band gap calculations), but a complete understanding is missing. Taking into account many-body effects and spin-orbit coupling we will determine the band structure of the high- and low-temperature phases and analyse the origin of the discrepancies. We will also investigate whether it is possible to induce a topological transition by applying hydrostatic pressure.