The Formation of Population III Protostars The formation of Population III stars is a well-posed problem, in that the initial conditions are specified by the cosmological standard model and extraordinarily well probed by observations of the cosmic microwave background radiation, galaxy surveys and many other means. Using the adaptive mesh refinement code Enzo, we follow the collapse of several 10^6 solar mass halos from cosmological initial conditions through protostellar densities, achieving unprecedented resolution of sub-solar radius, with over 30 levels of refinement. We developed a high density chemistry and radiation model that includes the effects of chemical heating and cooling, collision induced emission as well as optical depth effects of the molecular line and continuum transfer. Our calculations are able to follow the gas from cosmological scales to the AU scales when the protostar becomes optically thick to radiation and is able to contract only adiabatically (densities of 10^19 cm^-3). We find that the accretion rates are affected by the molecular hydrogen formation and destruction rates, and we see variation of nearly an order of magnitude on length scales of 10-200 AU, at which accretion disks are seen to form. We suggest that quantum chemical calculations as well as laboratory measurements of the molecular hydrogen three body formation rate will be needed to decide details of the population III protostar forming process. The mass of the protostar formed at one percent of a solar mass is indeed what had been found previously in one dimensional calculations. The accretion shock, however, is not spherical, and a disk geometry leads to hot, atomic shocked material in the polar regions. In summary, it is now possible to study the formation of population III protostars starting from cosmological initial conditions, covering 12 magnitudes in scale and 22 magnitudes in density.