Béla Bollobás, Extremal Graph Theory (Academic Press, 1978), 488 pp., £19·50.
Ian Muir Anderson · Proceedings of the Edinburgh Mathematical Society · 1980
The author attempts to cover his subject comprehensively in a short book.To this end, he omits proofs and, indeed, any indication of the techniques involved.He gives references to the literature for all proofs.As a result, the reader who wishes to get the full flavour of the subject will need access to a well-stocked library.The book is in three sections.The first two concern, respectively, geometrical and combinatorial problems for a single lattice.The third concerns problems on sets of lattices.In each section, there is a wide range of classical results, each with the subsequent refinements and generalisations, and with related open questions.Given the nature of the presentation, the book is unsuitable as an introduction to the subject, but it should have some appeal to those who have a knowledge of the geometry of numbers. W. W. STOTHERS