  In this thesis we classify modules over a Witt-type Lie algebra and
superalgebra such that when considered as modules of
$\mathcal{U}(\mathfrak{h})$ they are free of rank 1. We provide sufficient
conditions for simplicity, and compute the action of an automorphism on the
module. Lastly, we apply the weighting functor and show that the resulting
modules are intermediate series modules.
