A Research Trimester on Phase Space Analysis of Partial Differential Equations was held at the Centro di Ricerca Matematica “Ennio De Giorgi” during the period February 15 --- May 15, 2004. In the two volumes some of the contributions have been collected. The contributions are in the following different fields: Microlocal analysis, Fluid mechanics, Hyperbolic equations, Strichartz estimates, Other related fields (Uniqueness, Schrödinger operators, Hypoellipticity).