One of the biggest challenges in modern cosmology is to understand the first generation of stars and galaxies that formed during the cosmic Dark Ages. Since they reside in the observationally unexplored territory, we need to predict the properties of the first galaxies by pushing numerical simulations to new levels of physical realism and detail.  In this talk, I will present the results of our highly-resolved cosmological ab-initio simulations to understand the assembly process of first galaxies under the feedback from the first generation of stars, the so-called Population III. Also, I will illustrate how first galaxies can be connected with their local descendants in terms of chemical abundances in the local ultra-faint dwarf galaxies.