More than thirty years have passed since the detection of Gamma-Ray Bursts (GRBs) was first reported and enormous observational and theoretical efforts have been devoted to understanding this enigmatic phenomenon. Today, the GRB enigma, once one of the greatest mysteries in astrophysics, is partially solved: GRBs are the death throes of massive stars and the birth cries of black holes. Yet these objects continue to fascinate astronomers and the general public due to their unparalleled brilliance, the amazing relativistic bulk Lorentz factors involved, and because the conditions that lead to a GRB are still mysterious. What makes a massive star produce a GRB rather than a supernova? In this focused proposal, we concentrate on issues related to the geometry of the ejecta as a jet. We propose to construct, for the first time, relativistic two-dimensional self-similar hydrodynamic solutions. We will utilize these solutions to better understand relativistic jets, their lateral spreading and their interaction with the surrounding medium. Our research will illuminate the energetic content of the events, explore their geometrical diversity, and more accurately determine how frequent they are in the universe. We will explore an innovative way to identify orphan afterglows using the upcoming satellite GLAST.