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[Abstract]
This is an advanced graduate level textbook, designed both as an introduction for students to the subject of Hochschild cohomology, and as a resource for mathematicians who use Hochschild cohomology in their work. The text begins with definitions, properties, and many examples. The structure of Hochschild cohomology as a Gerstenhaber algebra is explored in detail. Many other topics of current interest are presented, including smoothness and duality, algebraic deformation theory, infinity structures, support varieties, and connections to Hopf algebra cohomology. Also included is an appendix containing some needed homological background.
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