  A general theory of permutation orbifolds is developed for arbitrary twist
groups. Explicit expressions for the number of primaries, the partition
function, the genus one characters, the matrix elements of modular
transformations and for fusion rule coefficients are presented, together with
the relevant mathematical concepts, such as Lambda-matrices and twisted
dimensions. The arithmetic restrictions implied by the theory for the allowed
modular representations in CFT are discussed. The simplest nonabelian example
with twist group S_3 is described to illustrate the general theory.
