In this thesis, we utilize novel radiation transfer technique called SimpleX to study complex ionization and dissociation processes in Population III star formation around 400 million years after the Big Bang. The first part describes the SimpleX method and its implementation as a radiation transfer code SPRAI in the hydrodynamic code Arepo. We test it on several standard test cases and demonstrate its usability for physically accurate calculations in the astrophysical context. The second part presents our model of first-star formation and discuss our results. We follow the collapse of the primordial gas cloud in the central regions of a minihalo. The collapse of the gas is evolved until the first stars form in the densest regions. Subsequently, we cut out the central four parsecs region of the simulation around the star- forming area, continue the simulation for the next 20 kyrs, and simulate radiation feedback from individual stars. The results show that the effect of the ionizing radiation strongly depends on the starting position of the escaping photons and resolution. Simulations in the previous literature neglect accretion disks within the inner 10 AU around the stars. Our simulations show that the lack of resolution leads to an overestimation of the escaping ionizing photons from the accreting Population III stars. We report the trapping of the ionizing radiation on the scale length of the height of the accretion disk