The subject of this thesis is beam dynamics in the Fermilab Booster at low energy, with emphasis on a realistic treatment of space charge effects. At the injection energy of 200 MeV in the Booster, the forces due to the self-field of the proton beam strongly perturb the motion, limiting the achievable phase space density. The tracking program TEAPOT is adapted to simulate this beam behavior in order to elucidate the causes of observed limitations on beam intensity and brightness. The model includes the effects of space charge, rf, acceleration, gradient errors and sextupoles. The evolution of beam intensity and emittances in the initial milliseconds following injection is examined in the model and compared with the behavior of the real beam for various input parameters. It is shown that the proximity of the half-integer resonance is responsible for most of the beam growth in the real machine, while an intrinsic space charge limit at the integer tune also exists. The model is also used to extrapolate the performance of the Booster to 400 MeV, which is to be the output energy of the upgraded Fermilab Linac, and the Booster is projected to satisfy the emittance and intensity requirements of the Main Injector at the higher injection energy.