  In 1981, Andr\'e Joyal provided a combinatorial interpretation of the algebra
of formal power series, a central gadget in the toolkit of enumerative
combinatorics. In Joyal's theory of species of structures, combinatorial
species (like permutations, graphs, partitions, etc.) are incarnated in
endofunctors on the category of finite sets and bijections. Species can be
added, multiplied, composed and differentiated; new species arise as solutions
to functional and differential equations. Moreover, everything achieved at the
level of species can be directly translated into the language of generating
series for enumeration of labelled, as well as unlabelled structures. More
recently, Labelle and Lamathe developed a general theory of differential
operators on species of structures, such as cycles or diagrams of derivatives.
The main goal of this dissertation is to present some parts of this theory.
