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This BCAM SpringerBriefs is a treaty of the§Infinity-Laplace Equation, which has inherited many features from the§ordinary Laplace Equation, and is based on lectures by the author. The§Infinity-Laplace Equation has delightful counterparts to the Dirichlet§integral, the mean value property, the Brownian motion, Harnack's inequality,§and so on. This "fully non-linear" equation has applications to image§processing and to mass transfer problems, and it provides optimal Lipschitz§extensions of boundary values. §§