Gamma-ray bursts (GRBs) are the mysterious, short and intense flashes of gamma-rays in the space, and are believed to originate from the rare, explosively devastating, stellar events that happens at cosmological distances. This book is a doctoral dissertation summarizing the author and collaborators' studies on various physical processes in GRBs. The topics and the findings from the studies are: the distribution of electrons' energy spectral index in GRBs and other relativistic sources is inconsistent with the prediction from the first-order Fermi theory of the shock particle acceleration;...