  This work is devoted to the geometric approach to supergravity. More
precisely, we interpret $\mathcal{N}=1$, $D=4$ supergravity as a super Cartan
geometry which provides a link between supergravity and Yang-Mills theory. To
this end, we first review important aspects of the theory of supermanifolds and
we establish a link between various different approaches. We then introduce
super Cartan geometries using the concept of so-called enriched categories.
This, among other things, will enable us to implement anticommutative fermionic
fields. We will then also show that non-extended $D=4$ supergravity naturally
arises in this framework. Finally, using this gauge-theoretic interpretation as
well as the chiral structure of the underlying supersymmetry algebra, we will
derive graded analoga of Ashtekar's self-dual variables and interpret them in
terms of generalized super Cartan connections. This gives canonical chiral
supergravity the structure of a Yang-Mills theory with gauge supergroup similar
to the self-dual variables in ordinary first-order Einstein gravity which was
first observed by F\"ul\"op \cite{Fulop:1993wi}. We then construct the parallel
transport map corresponding to the super connection in mathematical rigorous
way using again enriched categories. This provides the possibility of
quantizing gravity and matter degrees of freedom in loop quantum gravity in a
unified way.
