  We study the dynamics of an arbitrary semigroup of transcendental entire
functions using Fatou-Julia theory. Several results of the dynamics associated
with iteration of a transcendental entire function have been extended to
transcendental semigroups. We provide some conditions for connectivity of the
Julia set of the transcendental semigroups. We also study finitely generated
transcendental semigroups, abelian transcendental semigroups and limit
functions of transcendental semigroups on its invariant Fatou components.
