The formation of the first galaxies and the transition to low-mass star formation

The formation of the first galaxies at redshifts z similar to 10 - 15 signaled the transition front the simple initial state of the universe to one of ever increasing complexity. We here review recent progress in understanding their assembly process with numerical simulations, starting with cosmological initial conditions and modelling the detailed physics of star formation. In this, context we emphasize the importance and influence of selecting, appropriate initial conditions for the star formation process. We revisit the notion of a critical metallicity resulting in the transit,ion from primordial to present-day initial mass functions and highlight, its dependence on additional cooling mechanisms and the exact, initial conditions. We also review recent work oil the ability of dust cooling to provide the transition to present.-day low-mass, star formation. In particular, we highlight the extreme conditions under which this transition mechanism occurs with violent fragmentation in dense gas resulting in tightly packed clusters.