Proton Compton scattering has been studied from 220 to 330 MeV at 90 degree center of mass scattering angle with the polarized photon beam at LEGS. Compton scattering is an important probe of the nucleon structure and its excited states. Polarization degrees of freedom reveal more information than unpolarized observables. This experiment measured, for the first time, the polarized cross sections of proton Compton scattering up to the Δ resonance. The parallel and perpendicular cross sections were measured at the same time. All the photons were tagged so that the energy dependent systematic errors are small. The measured unpolarized cross section is above the lower bound from unitary at all energies. The cross section asymmetry is obtained as a function of energy for the first time. The unpolarized cross section is compared with previous data and with calculations from the fixed-t dispersion model, the isobar model and the finite energy dispersion model. Although all these calculations agree fairly well with unpolarized cross section data, the photon asymmetry data show that the isobar model contains serious defects. The ratio of polarized cross sections, dσ_⫫/dσ_⟂, is compared with a model independent result. The results from the present experiment can be used in the calculation of the E2/M1 ratio in the N — Δ transition, which is an important signature of the tensor interaction between quarks. / Ph. D.