Hello everybody, I would like to know about the work of Élie Cartan of PDE's that relate to the theory of foliations and differential forms.
I am interested in the subject and will be happy to receive basic references on the subject (articles) as well as explanations on the importance of the subject in mathematics today.
Best Answer
Robert Bryant is the reigning expert on this. An excellent book on the subject (later than the one mentioned) is: Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, Chicago Lectures in Mathematics (2003), University of Chicago Press (vii+213 pages, ISBN: 0-226-07794-2.) by R. Bryant, Phillip Griffiths and Dan Grossmann.
I just recalled, Bryant has a very nice set of nine introductory lectures on the subject. It may be just what you are looking for! They are available online here:
https://services.math.duke.edu/~bryant/Introduction_to_EDS.pdf