The publication of the first edition ofLagerungen in der Ebene, auf der Kugel und im Raumin 1953 marked the birth of discrete geometry. Since then, the book has had a profound and lasting influence on the development of the field. It included many open problems and conjectures, often accompanied by suggestions for their resolution. A good number of new results were surveyed by László 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...