| Summary: | This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. Key topics include: * Operators as "sums of squares" of real and complex vector fields: both analytic hypoellipticity and regularity for very low regularity coefficients; * Nonlinear evolution equations: Navier<U+0013>Stokes system, Strichartz estimates for the wave equation, instability and the Zakharov equation and eikonals; * Local solvability: its connection with subellipticity, local solvability for systems of vector fields in Gevrey classes; * Hyperbolic equations: the Cauchy problem and multiple characteristics, both positive and negative results. Graduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource. List of contributors: L. Ambrosio N. Lerner H. Bahouri X. Lu S. Berhanu J. Metcalfe J.-M. Bony T. Nishitani N. Dencker V. Petkov S. Ervedoza J. Rauch I. Gallagher M. Reissig J. Hounie L. Stoyanov E. Jannelli D. S. Tartakoff K. Kajitani D. Tataru A. Kurganov F. Treves G. Zampieri E. Zuazua
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