In this book we give an overview of major results, methods and ideas of convex and
discrete geometry and their applications. Besides being a graduate-level introduction
to the field, the book is a practical source of information and orientation for convex
geometers. It should also be of use to people working in other areas of mathematics
and in the applied fields.
We hope to convince the reader that convexity is one of those happy notions of
mathematics which, like group or measure, satisfy a genuine demand, are sufficiently
general to apply to numerous situations and, at the same time, sufficiently special to
admit interesting, non-trivial results. It is our aim to present convexity as a branch of
mathematics with a multitude of relations to other areas