  A basic principle of physics is the freedom to locally choose any unit system
when describing physical quantities. Its implementation amounts to treating
Weyl invariance as a fundamental symmetry of all physical theories. In this
thesis, we study the consequences of this "unit invariance" principle and find
that it is a unifying one. Unit invariance is achieved by introducing a gauge
field called the scale, designed to measure how unit systems vary from point to
point. In fact, by a uniform and simple Weyl invariant coupling of scale and
matter fields, we unify massless, massive, and partially massless excitations.
As a consequence, masses now dictate the response of physical quantities to
changes of scale. This response is calibrated by certain "tractor Weyl
weights". Reality of these weights yield Breitenlohner-Freedman stability
bounds in anti de Sitter spaces. Another valuable outcome of our approach is a
general mechanism for constructing conformally invariant theories. In
particular, we provide direct derivations of the novel Weyl invariant
Deser--Nepomechie vector and spin three-half theories as well as new higher
spin generalizations thereof. To construct these theories, a "tractor calculus"
coming from conformal geometry is employed, which keeps manifest Weyl
invariance at all stages. In fact, our approach replaces the usual Riemannian
geometry description of physics with a conformal geometry one. Within the same
framework, we also give a description of fermionic and interacting
supersymmetric theories which again unifies massless and massive excitations.
