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This book contains the proceedings of the AMS Special Session on Vertex Algebras and Geometry, held from October 8-9, 2016, and the mini-conference on Vertex Algebras, held from October 10-11, 2016, in Denver, Colorado. The papers cover vertex algebras in connection with geometry and tensor categories, with topics in vertex rings, chiral algebroids, the Higgs branch conjecture, and applicability and use of vertex tensor categories.