  The general theory of (nonlinear) partial differential equations originated
by S. Lie had a significant development in the past 30-40 years. Now this
theory has solid foundations, a proper language, proper techniques and
problems, and a wide area of applications to physics, mechanics, to say nothing
about traditional mathematics. However, the results of this development are not
yet sufficiently known to a wide public. An informal introduction in a
historical perspective to this subject presented in this paper aims to give to
the reader an idea about this new area of mathematics and, possibly, to attract
new researchers to this, in our opinion, very promising area of modern
mathematics.
