The primordial abundance of elements in the Universe is dominated by H and He. Heavier elements are only produced in stars during subsequent star formation episodes and dispersed into the ambient medium via supernovae explosions or stellar winds. The enrichment of the inter-stellar-medium by heavy elements plays a crucial role in the kind of stars formed and in the evolution of galaxies. Our aim is to simulate the different stages of enrichment on galactic scales and predict the properties of galaxies and their stars.

It is reasonably well established that the very first generation of stars should be characterised by massive objects with typical masses much larger than the presently observed ones. These primordial stars (Populations III stars) are formed out of pristine gas, where the cooling agents are limited to primordial, H-based molecules only, e.g. H_2 and HD. Therefore, masses of primordial stars should be quite high with a spectrum commonly referred to as a ``top-heavy'' initial mass function (IMF). Such massive stars have very short lifetimes (up to ~10^6 years only) and die mostly as black holes. The only range where primordial stars can explode as pair-instability supernovae (PISN) and pollute the surrounding medium is 140-260 solar masses. Despite the many uncertainties on their characteristics, population III stars have an important impact on the evolution of the intergalactic medium by initiating the metal pollution of the IGM, with the consequence of changing its chemical composition and the  related cooling properties (chemical feedback). As a consequence star formation events in enriched regions will happen under completely different conditions, with metals allowing further cooling and fragmentation to smaller mass scales. This results in an initial stellar-mass function peaked at lower masses and similar to the nowadays observed Salpeter-like IMF for Population II-I stars.

A very debated issue is the transition from the primordial pop III star formation regime to the standard popII-I regime. There is evidences for the existence of a critical metallicity, Z_crit, at which star formation allows such transition, but its exact value is not well-established yet, and we aim on deepening our understanding by investigating the difference in the consequences for proto-galaxies arising from various assumptions for Z_crit.

The chemical enrichment of the Universe is an in-homogeneous process, with some regions being enriched by the supernovae and galactic winds earlier than others. Therefore, the formation of stars and galaxies from unenriched, primordial gas is likely to take place over a range of redshifts, perhaps even extending down to z < 6 in rare regions of the Universe.  Population III star clusters that form this late in cosmic history may present the best chances of being found by future missions such as the James Webb Space Telescope and the European Extremely Large Telescope.