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This book is a collection of lecture notes and survey papers based on the minicourses given by leading experts at the 2016 CRM Summer School on Spectral Theory and Applications, held from July 4-14, 2016, at Universite Laval, Quebec City, Quebec, Canada. The papers contained in the volume cover a broad variety of topics in spectral theory, starting from the fundamentals and highlighting its connections to PDEs, geometry, physics, and numerical analysis.