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I discuss current theoretical expectations of how primordial, Pop III.1 starsform. Lack of direct observational constraints makes this a challenging task.In particular predicting the mass of these stars requires solving a series ofproblems, which all affect, perhaps drastically, the final outcome. While thereis general agreement on the initial conditions, H_2-cooled gas at the center ofdark matter minihalos, the subsequent evolution is more uncertain. Inparticular, I describe the potential effects of dark matter annihilationheating, fragmentation within the minihalo, magnetic field amplification, andprotostellar ionizing feedback. After these considerations, one expects thatthe first stars are massive >~100Msun, with dark matter annihilation heatinghaving the potential to raise this scale by large factors. Higher accretionrates in later-forming minihalos may cause the Pop III.1 initial mass functionto evolve to higher masses.

Population III.1 stars: formation, feedback and evolution of the IMF