  This thesis deals with the algorithmic representation of constructible
sheaves of abelian groups on the \'etale site of a variety over an
algebraically closed field, as well as the explicit computation of their
cohomology. We describe three representations of such sheaves on curves with at
worst nodal singularities, as well as algorithms performing various operations
(kernels and cokernels of morphisms, pullback and pushforward, internal Hom and
tensor product) on these sheaves. We present an algorithm computing the
cohomology complex of a locally constant constructible sheaf on a smooth or
nodal curve, which in turn allows us to give an explicit description of the
functor $\mathrm{R}\Gamma(X,-)\colon
\mathrm{D}^b_c(X,\mathbb{Z}/n\mathbb{Z})\to
\mathrm{D}^b_c(\mathbb{Z}/n\mathbb{Z})$. This description is functorial in the
scheme $X$ and the given complex of constructible sheaves. In particular, if
$X$ and the sheaf $\mathcal{F}$ are obtained by base change from a subfield, we
describe the Galois action on the complex $\mathrm{R}\Gamma(X,\mathcal{F})$. We
give precise bounds on the number of operations performed by the algorithm
computing $\mathrm{R}\Gamma(X,\mathcal{F})$. We also give an explicit
description of cup-products in the cohomology of locally constant constructible
sheaves over smooth projective curves. Finally, we show how to use these
algorithms in order to compute the cohomology groups of a constant sheaf on a
smooth surface fibered over the projective line.
