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The Extended Phase Graph (EPG) Algorithm is a powerful tool for magnetic resonance imaging (MRI) sequence simulation and quantitative fitting, but simulators based on EPG are mostly written to run on CPU only and (with some exception) are poorly parallelized. A parallelized simulator compatible with other learning-based frameworks would be a useful tool to optimize scan parameters, estimate tissue parameter maps, and combine with other learning frameworks. In this thesis, I present our work on an open source, GPU-accelerated EPG simulator written in PyTorch. Since the simulator is fully differentiable by means of automatic differentiation, it can be used to take derivatives with respect to sequence parameters, eg flip angles, as well as tissue parameters, eg T₁ and T₂. Here, I describe the simulator package and demonstrate its use for a number of MRI tasks including tissue parameter estimation and sequence optimization.