Alexander Barvinok, University of Michigan, Ann Arbor, MI.

• ChaptersChapter 1. Convex sets at largeChapter 2. Faces and extreme pointsChapter 3. Convex sets in topological vector spacesChapter 4. Polarity, duality and linear programmingChapter 5. Convex bodies and ellipsoidsChapter 6. Faces of polytopesChapter 7. Lattices and convex bodiesChapter 8. Lattice points and polyhedra

An excellent choice of textbook for a geometry course ... Everything the reader needs is defined in the book ... The chapters are well integrated ... I enthusiastically recommend [the book]. It effectively demonstrates how convexity connects with just about all branches of mathematics. The book is well illustrated and well written ... In reading it, I get the sense of how enjoyable it would be to hear Barvinok lecture on the material. I hope that it will attract many students to this branch of geometry."" - MAA Monthly""My impression is that the book would be fine to teach from ... it contains many useful diagrams. The test is well written, and everything is clearly explained ... wealth of material that it contains and the excellence of its treatment would make this book a desirable addition to one's library. I recommend it highly."" - Bulletin of the LMS