Abstract: In the present thesis, it is introduced for the observed characters and physical processes of the gamma-ray burst. Then, the hydrodynamic evolution and synchrotron mechanism of fireball / blast wave model are discussed. The hydrodynamic evolution of the fireball shell is comprehensively studied. Using the synchrotron mechanism and relativistic transformation from co-moving frame to lab frame, the light curves of the gamma-ray burst afterglow are obtained. These light curves are different for various dynamic evolution of the shell, isotropic or anisotropic cases and various environment of the media. Through comparing these different light curves, the whole physical evolution of the gamma-ray burst afterglow and the various physical processes effecting on the evolution of the gamma-ray burst afterglow are presented.