  The theory of supercharacters, recently developed by Diaconis-Isaacs and
Andre, can be used to derive the fundamental algebraic properties of Ramanujan
sums. This machinery frequently yields one-line proofs of difficult identities
and provides many novel formulas. In addition to exhibiting a new application
of supercharacter theory, this article also serves as a blueprint for future
work since some of the abstract results we develop are applicable in much
greater generality.
