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In May 2006, The University of Utah hosted an NSF-funded minicourse on shastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to various modern topics in shastic PDEs, and to bring together several experts whose research is centered on the interface between Gaussian analysis, shastic analysis, and shastic partial differential equations. This monograph contains an up-to-date compilation of many of those lectures. Particular em...