  The variant of a semigroup S with respect to an element a in S, denoted S^a,
is the semigroup with underlying set S and operation * defined by x*y=xay for
x,y in S. In this article, we study variants T_X^a of the full transformation
semigroup T_X on a finite set X. We explore the structure of T_X^a as well as
its subsemigroups Reg(T_X^a) (consisting of all regular elements) and E_X^a
(consisting of all products of idempotents), and the ideals of Reg(T_X^a).
Among other results, we calculate the rank and idempotent rank (if applicable)
of each semigroup, and (where possible) the number of (idempotent) generating
sets of the minimal possible size.
