An algebraic stack over a scheme 
is a stack in groupoids on the faithfully flat, locally finitely
presented topology of 
-schemes, whose diagonal is representable by algebraic
spaces and which admits a smooth surjective presentation by a scheme.
The presentation is also called a smooth atlas (Stacks Project, Definition 94.12.1).
The groupoids retain automorphisms of the parametrized objects. A scheme
or an algebraic space is an example with trivial
automorphism groups.
For a smooth projective curve 
and an algebraic group 
, the stack 
parametrizes principal 
-bundles and their isomorphisms.
Categories of sheaves or D-modules
on such bundle stacks enter the geometric and quantum geometric Langlands correspondences.
