The aim of this proposal is to simulate the formation and evolution of galaxies within the first billion years of the Universe by using unprecedented high-resolution simulations. The hydrodynamical, cosmological simulations are designed to evolve the Universe, focusing on the sites of star and galaxy formation. They include all the relevant physics: radiative cooling and formation of molecular hydrogen, star formation and feedback from supernovae, metal enrichment of the inter-stellar material, black hole formation and feedback. In particular, the theory of population III (POP III) star formation will be tested within a cosmological framework. The reseracher would like to address the following questions: (i) what is the luminosity function of galaxies at redshift six and larger; (ii) how the transition from metal poor POP III to metal enriched POP II star formation happens; (iii) what is the role of the turbulence from cold accretion in mod ifying star formation at early times; (iv) where seed black holes from POP III stars form and how they grow. Answering these questions will deepen the understanding of the formation of the first galactic structures in the Universe, and will provide direct predictions for upcoming space-based satellite missions like the James Webb Space Telescope.