Differential Galois theory as originally proposed in the early 1900s and then developed by Kolchin, was designed as a counterpart to the usual algebraic Galois theory to show that certain differential equations cannot be solved in terms of solutions to certain other equations.

Given a differential field extension L/K, the differential Galois group of this extension (if it exists!) is a differential algebraic group G over K for which G(K) may be naturally identified with Aut(L/K).

For example, if L is generated over K by a solution a to the differential equation X' = t where t ∈ K - {0}, then the differential Galois group is the additive group of the constant field.

Poizat suggested that the differential Galois group may be understood in terms of binding groups and Pillay developed these details in the most general case.