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In this paper, the classical and quantum theory of $\mathcal{N}=1$supergravity in four spacetime dimensions will be studied in the framework ofloop quantum gravity. We discuss the canonical analysis of the supergravityHolst action as first introduced by Tsuda. In this way, we also derive acompact expression of the supersymmetry constraint, which plays a crucial rolein canonical supergravity theories, akin to the role of the Hamiltonianconstraint in non-supersymmetric generally covariant theories. The resultingtheory is then quantized using loop quantum gravity methods. In particular, wepropose and discuss a quantization of the supersymmetry constraint and deriveexplicit expressions of the action of the resulting operator. This is importantas it is the first step on the way of analyzing the Dirac algebra generated bysupersymmetry and Hamiltonian constraint in the quantum theory and for findingphysical states. We also discuss some qualitative properties of such solutionsof the SUSY constraint.

$\mathcal{N}=1$ Supergravity with LQG methods and quantization of the SUSY constraint