 The specification of gluings requires a definition of coverings with regard to which the gluings can be considered.It turns out that the general language for describing these coverings is that of a Grothendieck topology.Thus a stack is formally given as a fibred category over another "base" category, where the base has a Grothendieck topology and where the fibred category satisfies a few axioms that ensure existence and uniqueness of certain gluings with respect to the Grothendieck topology.