Gamma-ray bursts (GRBs) and supernovae (SNe) are two of the most spectacular types of cosmic explosions in the transient sky. Both phenomena are associated with the death of massive stars or disruption of compact objects. Our knowledge of these events is thus closely related to the understanding of stellar evolution across the universe. These energetic events are also used as probes of the ionization and star formation history and powerful tools to measure the cosmic expansion. This thesis presents the follow-up observations of GRBs and the discoveries of SNe by the ROTSE-III robotic optical systems. With automated operation and fast slewing, ROTSE-III has made unique contributions to the study of GRBs by providing very early optical observations. A large fraction of ROTSE-III's burst responses started during the gamma-ray emission phase. These ``prompt'' optical detections and limits are invaluable for constraining the burst properties and the immediate environment surrounding the progenitor. I discuss examples of multi-wavelength studies of GRBs with an emphasize on the transition phase from the burst to the afterglow. The ROTSE Supernova Verification Project (RSVP) is an extension of the effort initiated by the Texas Supernova Search (TSS). By scanning a large portion of the sky nightly without bias towards bright galaxies, RSVP discovered over 40 SNe in about two years and a relatively large fraction of peculiar events. Among these, two SNe, 2008am and 2008es, belong to the ultra-luminous type that was not known before TSS and one event, 2007if, was an over-luminous Type Ia SN and a candidate for a super-Chandrasekhar mass explosion. With ROTSE-III, we hope to discover and monitor more ultra-luminous SNe to understand their extraordinary energy output, whether they are powered by ejecta-circumstellar medium interactions or thermonuclear reactions triggered by pair instability. In the case of SNe Ia, it is not likely that a single parameter, e.g. the amount of radioactive nickel produced, is able to account for their diversity. Circumstellar medium interaction, as a probable source of excess luminosity, is investigated
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