  In this article we study the Picard functor and the Picard stack of an
algebraic stack. We give a new and direct proof of the representability of the
Picard stack. We prove that it is quasi-separated, and that the connected
component of the identity is proper when the fibers of the stack are
geometrically normal. We study some examples of Picard functors of classical
stacks. In an appendix, we review the lisse-etale cohomology of abelian sheaves
on an algebraic stack.
