A groupoid consists of a set of objects formula_23, a set of arrows formula_24, and structural maps including the source and the target maps formula_25 and other maps allowing arrows to be composed and inverted. It is called a Lie groupoid if both formula_23 and formula_24 are smooth manifolds, all structural maps are smooth, and both the source and the target maps are submersions. It is called proper if the map formula_28 is a proper map. It is called étale if both the source and the target maps are local diffeomorphisms. An orbifold groupoid is a proper étale Lie groupoid.