Lagerungen

The publication of the first edition ofLagerungen in der Ebene, auf der Kugel und im Raumin 1953 marked thebirth of discrete geometry.Since then, the book has had a profound and lasting influenceon the development of the field. It included many open problems and conjectures, often accompaniedby suggestions for their resolution. A goodnumber of new results were surveyed byLászló Fejes Tóth in hisNotesto the 2nd edition. The present version ofLagerungenmakes this classic monograph available in English for the first time, with updatedNotes,completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the originalLagerungen, the revised and updatedNotesonthe original text, eight self-contained chapters surveying additional topics in detail. The English edition provides a comprehensive update to an enduring classic. Combining the lucid exposition of the original text with extensive new material, it will be a valuable resource for researchers in discrete geometry for decades to come.