Massive, massless, and partially massless spin-2 fields

Spin-2 particles, or gravitons, present both virtues and vices not displayed by their lower spin peers. A massless graviton can only be described consistently by a single theory---general relativity---while mutual couplings among ``colored'' gravitons are simply not allowed. A massive graviton is also believed to admit a unique set of interactions, ones that are however pestered by superluminal perturbations and a rather limited effective field theory. And then there is the third member of the clique, the partially massless graviton, who lives in a universe with a naturally small cosmological constant, but which nonetheless seems not to exist at all. The aim of this thesis is to explore this enormously rich and tightly fettered realm of classical theories of spin-2 fields.