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This book determines whether the general member of each family of smooth Fano threefolds admits a Kähler-Einstein metric, using K-stability. Complemented by appendices outlining results needed to understand this active area, it will be essential reading for researchers and graduate students working on algebraic and complex geometry.

"This text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics, offering a new conceptual treatment of the twisting procedure. It includes many motivating examples to render the theory accessible to graduate students, as well as a survey of recent applications"--