  In this paper, using the correspondence of gentle algebras and dissections of
marked surfaces, we study full exceptional sequences in the perfect derived
category $\mathsf{K^b(A)}$ of a gentle algebra $\mathsf{A}$. We show that full
exceptional sequences in $\mathsf{K^b(A)}$ exist if and only if the associated
marked surface has no punctures and has at least two marked points on the
boundary. Furthermore, by using induction on cuts of surfaces, we characterise
when an exceptional sequence can be completed to a full exceptional sequence.
If the genus of the associated surface is zero then we show that the action of
the braid group together with the grading shift on full exceptional sequences
in $\mathsf{K^b(A)}$ is transitive. For the case of surfaces of higher genus,
we reduce the problem of transitivity to the problem of the existence of
certain sequences of pairs of exceptional objects. Finally, we interpret the
duality of a full exceptional sequence induced by the longest element in the
associated symmetric group using Koszul duality.
