This is my own version od a lecture with a similar title of M. Dafermos, delivered at Stony Brook. (September 20010) .

This is a special lecture in honour of F. John's 100 anniversary. (November 20010) .

This is a Bourbaki seminar on the work of Dafermos-Rodnianski. (November 2009) .

This is a general lecture delivered at the international conference `` Beyond Einstein'' in Mainz, September 2008.

The set of lectures delivered at the IPAM workshop in Oscillatory Integrals and PDE' March 19-25 2001, UCLA.

This is another philosophical lecture delivered at the AMS Millenium Conference in Los Angeles, August, 2000.

Geometric and Fourier Methods in Nonlinear Wave Equations (Lecture in Tel-Aviv, Aug, 1999).

This is a philosophical essay reflecting my personal views about PDE's. Published in the proceedings of the conference `` Visions in Mathematics'' Tel Aviv 1999.