Finite arrangements of convex bodies were intensively investigated in the second half of the twentieth century. Connections to many other subjects were made, including crystallography, the local theory of Banach spaces, and combinatorial optimisation. This book, the first one dedicated solely to the subject, provides an in-depth state-of-the-art discussion of the theory of finite packings and coverings by convex bodies. It contains various new results and arguments, besides collecting those scattered around in the literature, and provides a comprehensive treatment of problems whose interplay was not clearly understood before. In order to make the material more accessible, each chapter is essentially independent, and two-dimensional and higher-dimensional arrangements are discussed separately. Arrangements of congruent convex bodies in Euclidean space are discussed, and the density of finite packing and covering by balls in Euclidean, spherical and hyperbolic spaces is considered.

'Many of the sections end with interesting and stimulating open problems, and each chapter closes with a brief survey of related problems. The material is presented in a clear and concise way. The author has succeeded in providing a unified treatment of all these different threads of finite packing and covering problems. … All in all, however, this book is a unique and indispensable source for everyone interested in finite packing and covering of convex bodies.'

Source: Bulletin of the London Mathematical Society

' … a unique and indispensable source for everyone interested in finite packing and covering of convex bodies.'

Source: Bulletin of the LMS