The In-Medium Similarity Renormalization Group (IM-SRG) is an ab initio many-body method that has enjoyed increasing prominence in nuclear theory, due to its soft polynomial scaling with system size, and the flexibility to target ground and excited states of both closed- and open-shell systems. Despite many successful applications of the IM-SRG to microscopic calculations of medium-mass nuclei in recent years, the conventional formulation of the method suffers a number of limitations. Key amongst these are i) large memory demands that limit calculations in heavier systems and render the calculation of observables besides energy spectra extremely difficult, and ii) the lack of a computationally feasible sequence of improved approximations that converge to the exact solution in the appropriate limit, thereby verifying that the IM-SRG is systematically improvable. In this thesis, I present a novel formulation of the IM-SRG based on the Magnus expansion. I will show that this improved formulation, guided by intuition gleaned from a diagrammatic analysis of the perturbative content of different truncations and parallels with coupled-cluster theory, allows one to bypass the computational limitations of traditional implementations, and provides computationally viable approximations that go beyond the truncations used to date. The effectiveness of the new Magnus formulation is illustrated for several many-nucleon and many-electron systems.
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