This book provides a comprehensive description of advances in the study of general relativistic instability supernovae. These supernovae, if observed, would provide direct evidence of the existence of supermassive stars, thus confirming that massive seed black holes played a crucial role in the assembly of observed high redshift quasars. The book begins with a review of the history of and motivation for the study of supermassive stars. Supermassive stars are most likely to exist in the high redshift universe and are thus difficult to find. One possibility for observing these stars is the thermonuclear explosion occurring at the end of the lives of some supermassive stars. In order to model these explosions, the author first performs evolutionary simulations with a post Newtonian stellar evolution code HOSHI, evolves these simulations to the general relativistic radial instability, locating the instability using a normal mode analysis of the radial perturbations of the star in general relativity. Next, when the star becomes unstable, the author simulates the dynamics of the explosion or collapse to a black hole by transporting the model to a general relativistic Lagrangian hydrodynamics code with a nuclear network. The two main explosion mechanisms for these stars are the explosive alpha process and the CNO cycle and rapid proton capture process. If the model explodes, the nucleosynthetic ejecta and the light-curve are computed. For multiple types of supermassive stars, it is found that general relativistic instability supernovae are a general consequence of the existence of supermassive stars which are destabilized during their evolution by general relativity. These results run contrary to those of previous papers which found that these types of explosions were much rarer. The results are compared to existing James Webb Space Telescope data and prospects for observation using future instruments are discussed. The book is intended for physics and astronomy researchers interested in the origin and growth of massive black holes, the evolution and explosions of massive stars, and supernovae and chemical enrichment of the early universe.