Abstract
The full transformation semigroup is the semigroup analogue of the symmetric group. Any semigroup is isomorphic to a semigroup of transformations . This semigroup arises naturally in automata theory, a branch of theoretical computer science . The purpose of this thesis is to study the full transformation semigroup in a new way. We accomplish this by realizing that the full transformation semigroup is a subsemigroup of the monoid of all n × n matrices.This allows us to transfer Lie theoretic concepts to the full transformation semigroup. In particular we find analogues of Borel and parabolic subgroups, root elements and Chevalley’s big cell