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The formation of the first galaxies at redshifts z ~ 10-15 signaled thetransition from the simple initial state of the universe to one of everincreasing complexity. We here review recent progress in understanding theirassembly process with numerical simulations, starting with cosmological initialconditions and modelling the detailed physics of star formation. In thiscontext we emphasize the importance and influence of selecting appropriateinitial conditions for the star formation process. We revisit the notion of acritical metallicity resulting in the transition from primordial to present-dayinitial mass functions and highlight its dependence on additional coolingmechanisms and the exact initial conditions. We also review recent work on theability of dust cooling to provide the transition to present-day low-mass starformation. In particular, we highlight the extreme conditions under which thistransition mechanism occurs, with violent fragmentation in dense gas resultingin tightly packed clusters.

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