Abstract: In this series of 3 talks I will first state the general concept of a system of PDE's associated to a non-degenerate CR-manifold. The idea goes back to Lie, Cartan and Segre, and it was undeservedly forgotten. The PDE-approach was recently reviewed by A.Sukhov and J.Merker and enabled the latter one to obtain some interesting results in CR-geometry. The classical results of S.Lie and the recent results of J.Merker will be stated on the second lecture. Finally, on the last lecture I will tell about a recent result with R.Shafikov concerning extension of holomorphic mappings where the PDE-approach was successfully applied as well.