  In this thesis, we study extensions of the theory of Riemannian submanifolds
in two directions. First, we will show how Riemannian geometry and submanifold
theory in particular, can be generalized using the notion of 'Rinehart spaces',
and it will be demonstrated how the developed framework unifies some existing
and new flavours of Riemannian geometry over different ground rings. In the
second part of the thesis, we give a description of holomorphic Riemannian
submanifold theory where complex numbers fully replace the role of the real
numbers as ground field, and show how this can be applied to reveal direct
connections between the submanifolds of so-called Wick-related
pseudo-Riemannian spaces.
