  In this thesis, we attempt to gain a more complete insight into Double Layer
Theories in Weyl Gravity. In order to do this, we first establish the premise
of Weyls Theory, including its provenance, development and flaws. This is all
discussed in the first five chapters of the thesis. After having established
Weyls Infinitesimal geometry and his gauged (scalar-tensor) gravity theory, we
move onto the topic at hand, namely, Double Layers. We define the action to be
used and describe the volume of integration (especially the Singular Hyper
Surface) across which the action principle is setup. We define our gauss Normal
Coordinate system and the scheme which we follow when we undertake our
calculation. The following sections detail the variation process, in a succinct
manner, taking turn by turn, each of the four parameters of our Quadratic
Lagrangian. In the last chapter, we conclude the thesis by gleaning out the
meaning behind our newfound surface energy tensor terms and what they might
imply physically, as well as drawing a clearer picture of contrast between
General Relativity and Weyl gravity.

General Relativity and Quantum Cosmology