  In this note, we present a few existence theorems for the quotient of a
scheme by the action of a group. The first two sections are devoted to
Grothendieck topologies and descent theory. The third one is dealing with
quotients: we first give direct and (almost) complete proofs for the main
existence results of SGA 3, expos\'e V. Then we discuss some specific
situations: the quotient of an algebraic group over a field by a subgroup, the
quotient of a group by the normalizer of a smooth subgroup, and quotients of
affine schemes by free actions of diagonalizable groups. From place to place,
the original proofs have been slightly improved (e.g. with the use of algebraic
spaces). This note grew out of lectures given by the author in the CIRM
(Luminy) during the Summer School "Sch\'emas en groupes" in 2011.
