  This text is my thesis, defended in June 2007, in the status it was at this
time. The most important results are contained in the article "Foncteur de
Picard d'un champ alg\'ebrique" to appear in "Mathematische Annalen" (see the
preprint arXiv:0711.4545). In the article, some results have been added, and
some previous results have been strengthened. However, the proofs of the
results contained in the appendix (concerning the smooth-\'etale cohomology on
an algebraic stack) have been removed. The thesis is only put on the ArXiv to
provide a more lasting reference than my webpage for these proofs.
