The book under review gives an excellent, self-contained, and unified approach to some classical and very recent results and advances in the enumeration of integer points in polyhedra. This unified point of view is based on valuations on, roughly speaking, the algebra of polyhedra, and so the first chapters provide an introduction to this algebra and to some geometric as well as combinatorial properties of polyhedra, e.g., the Euler-Poincare formula or the decomposition theorem of polyhedra, which states that, modulo polyhedra containing lines, a polyhedron is just the sum of its tangent cones at the vertices

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