The publication of the first edition of  Lagerungen in der Ebene, auf der Kugel und im Raum  in 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 his  Notes  to the 2nd edition. The present version of  Lagerungen  makes this classic monograph available in English for the first time, with updated  Notes,  completed by extensive surveys of the state of the art. More precisely, this book consists of: a corrected English translation of the original  Lagerungen, the revised and updated  Notes  on the 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.