  String theory, specifically type-II superstring theory, can be formulated in
any ten-dimensional signature. To facilitate the study of supergravity and
superstring theories in this setting, we present a uniform construction of
supersymmetry algebras in arbitrary dimension and signature, which generalizes
the ideas underlying symplectic Majorana spinors. In our formalism R-symmetry
acts on an auxiliary multiplicity space which makes its action manifest. This
allows us to provide extensive tables which list the R-symmetry groups of
extended supersymmetry algebras for all signatures together with other useful
information. Twisted (`type-*') supersymmetry algebras in Lorentz signature
with non-compact R-symmetry groups are shown to be part of a general pattern
resulting from the interplay between complex superbrackets and reality
conditions. As an application we show how the relations between type-II string
theories in ten and nine dimensions can be extracted from their supersymmetry
algebras. We also use our results to determine the special geometry of vector
and hypermultiplet scalar manifolds of four-dimensional $\mathcal{N}=2$ and
three-dimensional $\mathcal{N}=4$ supergravity theories for all signatures.
