From the reviews:
"The aim of the present book is to give an overview of basic methods and results of convex analysis and discrete geometry and their applications. ... A large bibliography of 1052 titles, each of them being referred to in the text, tries to cover all the facets of the subject, from its origins to the present day state. ... the clear and pleasant style of presentation, make the book accessible to a large audience, including graduate students, teachers and researchers in various areas of mathematics." (S. Cobzas, Studia Universitatis Babes-Bolyai, Vol. LII (4), 2007)
"Convex geometry is a classical area of mathematics that dates back to antiquity. ... the author's main goal is to expose applications of convex geometry to other areas of mathematics and science, in particular number theory, mathematical physics, crystallography, tomography, optimization, and computational geometry. ... The book can be used for graduate courses in convex, discrete geometry and geometry of numbers. For experts and people working on applications, the book is a very valuable source of open problems, new directions and references." (Aleksandr Koldobsky, Mathematical Reviews, Issue 2008 f)
"This excellent book presents a complete and coherent overview of principal ideas, results and methods of convex and discrete geometry. ... The book is highly recommended to everyone who is interested in convex geometry: it may be viewed as a graduate-level introduction as well as a source of both classical and actual results in the subject." (Vasyl Gorkaviy, Zentralblatt MATH, Vol. 1139 (17), 2008)
"In this monograph, the author gives a broad and colourful picture of classic and contemporary convex geometry and discrete geometry. ... presents a wide variety of highly interesting and often surprising results. ... can be used as textbook for different courses in geometry. ... reader will find more and more results which he or she has not seen beforein a monograph and perhaps not even in the original literature. ... a book that addresses itself to a wider public and is accessible to students." (R. Schneider, International Mathematical News, Issue 12, December, 2009)
"This almost 600 page monograph introduces the reader to the present state of the theory of convex geometry in its many facts. ... All proofs are carefully chosen and presented with all details. ... The book will be appreciated by specialists in the field ... . The book can be used as a base for some special courses at universities and for further preparation of PhD students. It is a book that should be available in any mathematical oriented library." (EMS Newsletter, December, 2009)
"A fascinating overview of major results, methods and ideas of convex and discrete geometry and some of their applications. ... present this enormous amount of topics and results in a clear and lucid way by sprinkling the text with various comments, historic and heuristic remarks ... . All in all an impressive book, which by no means may serve only as work of reference but can be used very well as a rich source for lecturers and as graduate-level introduction to the field." (G. Kowol, Monatshefte fuer Mathematik, Vol. 156 (3), March, 2009)
