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Based on a graduate course given at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides complete proofs for most theorems.
The material requires only linear algebra as a prerequisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions.
The lectures - introduce the basic facts about polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids) - discuss important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associhedra, fiber polytopes, and the Lawrence construction) - show the excitement of current work in the field (Kalai´s new diameter bounds, construction of non-rational polytopes, (the Bohne-Dress tiling theorem, the upper-bound theorem)

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Preface.- Preface to the Second Printing.- Introduction and Examples.- Polytopes, Polyhedra, and Cones.- Faces of Polytopes.- Graphs for Polytopes.- Steinitz´ Theorem for 3-Polytopes.- Schlegel Diagrams for 4-Polytopes.- Duality, Gale Diagrams, and Applications.- Fans, Anrrangements, Zonotopes, and Tilings.- Shellability and the Upper Bound Theorem. Fiber Polytopes, and Beyond.- References.- Index.

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From the reviews:

"This is an excellent book on convex polytopes written by a young and extremely active researcher." (Acta Scientiarum Mathematicarum)

"From the publication of the first printing, in 1994, this book became one of the most widely used textbooks in Discrete Geometry. The reviewer sees at least two reasons for that: the beautiful mathematics presented here, and the fact that the book can be used at a wide variety of levels, for several different courses. ... It is not only students who can benefits from the book. Researchers will find its updates notes and references very helpful." (Miklós Bóna, MathDL, August, 2007)

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Günter M. Ziegler, 1963 in München geboren, studierte in München und am MIT Mathematik und wurde mit 31 der jüngste Professor an der TU Berlin. Ausgezeichnet mit dem Leibniz-Preis, dem höchsten deutschen Forschungspreis, sowie dem Communicator-Preis, begann er als Präsident der Mathematiker-Vereinigung und "Jahr der Mathematik"-Initiator eine große Charme-Offensive für sein Fach. Und die setzt er jetzt von der FU Berlin aus fort.

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