  We give an account of the theory of dessins d'enfants which is both
elementary and self-contained. We describe the equivalence of many categories
(graphs embedded nicely on surfaces, finite sets with certain permutations,
certain field extensions, and some classes of algebraic curves), some of which
are naturally endowed with an action of the absolute Galois group of the
rational field. We prove that the action is faithful. Eventually we prove that
this absolute Galois group embeds into the Grothendieck-Teichm\"uller group
$GT_0$ introduced by Drinfel'd. There are explicit approximations of $GT_0$ by
finite groups, and we hope to encourage computations in this area.
  Our treatment includes a result which has not appeared in the literature yet:
the Galois action on the subset of regular dessins - that is, those exhibiting
maximal symmetry -- is also faithful.
