It is a generalisation[dubious – discuss] of the concept of a group, originating however from the geometric approach of Sophus Lie[1] to investigate symmetries of differential equations, rather than out of abstract algebra (such as quasigroup, for example).
Manifolds with additional structures can often be defined using the pseudogroups of symmetries of a fixed local model.
Methods proposed by Lie and by Cartan for studying these objects have become more practical given the progress of computer algebra.
In the same decade the interest for theoretical physics of infinite-dimensional Lie theory appeared for the first time, in the shape of current algebra.
However, all these various approaches involve the (finite- or infinite-dimensional) jet bundles of Γ, which are asked to be a Lie groupoid.
In particular, a Lie pseudogroup is called of finite order k if it can be "reconstructed" from the space of its k-jets.