This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theory. Key topics: * The Cauchy problem for linear and nonlinear hyperbolic equations * Scattering theory * Inverse problems * Hyperbolic systems * Gevrey regularity of solutions of PDEs * Analytic hypoellipticity and unique features: * Original articles are self-contained with full proofs * Survey articles give a quick and direct introduction to selected topics evolving at a fast pace Graduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource.