Structure of Symmetry Groups via Cartan's Method: Survey of Four   Approaches
  In this review article we discuss four recent methods for computing Maurer-Cartan structure equations of symmetry groups of differential equations. Examples include solution of the contact equivalence problem for linear hyperbolic equations and finding a contact transformation between the generalized Hunter-Saxton equation and the Euler-Poisson equation. 
Oleg I. Morozov