  We define the operation of composing two hereditary classes of permutations
using the standard composition of permutations as functions and we explore
properties and structure of permutation classes considering this operation. We
mostly concern ourselves with the problem of whether permutation classes can be
composed from their proper subclasses. We provide examples of classes which can
be composed from two proper subclasses, classes which can be composed from
three but not from two proper subclasses and classes which cannot be composed
from any finite number of proper subclasses.
