This is an account of the algebraic geometry of Witt vectors and related
constructions. The theory of the usual, "p-typical" Witt vectors of p-adic
schemes of finite type is already reasonably well understood. The main point
here is to generalize this theory in two different ways. We allow not just
p-typical Witt vectors but also, for example, those taken with respect to any
set of primes in any ring of integers in any global field. In particular, this
includes the "big" Witt vectors.