  Dessin d'enfants (French for children's drawings) serve as a unique
standpoint of studying classical complex analysis under the lens of
combinatorial constructs. A thorough development of the background of this
theory is developed with an emphasis on the relationship of monodromy to
Dessins, which serve as a pathway to the Riemann Hilbert problem. This paper
investigates representations of Dessins by permutations, the connection of
Dessins to a particular class of Riemann surfaces established by Belyi's
theorem and how these combinatorial objects provide another perspective of
solving the discrete Riemann-Hilbert problem.
