This thesis is concerned with the study of various aspects of the Yang-Mills Squared construction, which aims at furthering our understanding of the provocative idea that gravity may be regarded, in some sense, as the "square" of gauge theory. By assuming a convolutive tensor product and introducing a bi-adjoint scalar fi eld as one of the factors, the Yang-Mills Squared formalism describes a purely field-theoretic realisation of this correspondence: the content as well as the global U-duality symmetries of a wide variety of supergravity theories may be shown to originate in the product of the contents and R-symmetries of two super Yang-Mills theories. Here we apply these ideas to twin supergravities, pairs of theories with identical bosonic sectors but di fferent supersymmetric completions, to demonstrate that they are related in a controlled fashion through the
underlying Yang-Mills factors. This has the additional advantage of giving a prescription
for constructing new examples of factorisable supergravities from known ones. The second part of the thesis is devoted to the study of the gauge symmetries of linearised axion-dilaton gravity by adopting a Becchi-Rouet-Stora-Tyutin (BRST) covariant formulation of Yang-Mills. The content, BRST and anti-BRST transformations as well as the
equations of motion of the gravitational side are shown to be related to those of the gauge
theory side by means of a dictionary building the gravity fields as sums of convolutions of Yang-Mills potentials and ghosts, thus providing a fully Lorentz-covariant version of the Yang-Mills Squared map. The anti-BRST transformations of the Kalb-Ramond 2-form sector are shown to naturally anti-commute with BRST in this formalism.