The content material of this booklet corresponds to a one-semester direction taught on the college of Paris-Sud (Orsay) within the spring 1994. it's available to scholars or researchers with a easy hassle-free wisdom of Partial Dif ferential Equations, particularly of hyperbolic PDE (Cauchy challenge, wave operator, strength inequality, finite velocity of propagation, symmetric structures, etc.). This direction isn't really a few ultimate encyclopedic reference collecting all avail capable effects. We attempted as a substitute to supply a brief man made view of what we think are the most effects received thus far, with self-contained proofs. in reality, a few of the most crucial questions within the box are nonetheless thoroughly open, and we are hoping that this monograph will supply younger mathe maticians the need to accomplish extra learn. The bibliography, limited to papers the place blowup is explicitly dis stubborn, is the one half we attempted to make as entire as attainable (despite the hot preprints circulating daily) j the references are commonly no longer pointed out within the textual content, yet within the Notes on the finish of every bankruptcy. simple references corresponding most sensible to the content material of those Notes are the books by way of Courant and Friedrichs [CFr], Hormander [HoI] and [Ho2], Majda [Ma] and Smoller [Sm], and the survey papers via John [J06], Strauss [St] and Zuily [Zu].
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