Lagerungen: Arrangements in the Plane, on the Sphere, and in Space

1953, the year the first edition of Lagerungen appeared in print, marks the birth of discrete geometry, a branch of classical geometry that deals with packing, covering, as well as an array of other arrangements, for their own sake, and not just as a tool for number theory. The contributions of L嫳zl?Fejes T鏒h to this new, exciting, and dynamically developing field are numerous and of fundamental importance. Lagerungen is a crowning summary of his most productive period in life. The book includes many open problems and conjectures, often accompanied by the Author's ideas of possible ways of approaching them. A good number of solutions appeared in between the 1st and 2nd Editions, surveyed by the Author in his Notes to the 2nd edition. More progress followed steadily during the next five decades. Undeniably, the book had a profound influence on the development of the theory, continuing today with undiminished vigor.
The present text consists of the following parts:
a) A translation of the original Lagerungen book, b) the Notes, that contain comments to the original text of the book, and c) eight self-contained chapters surveying material that is related to the subject of the original book, but is not mentioned in it.
This English translation of the original text with thoroughly updated notes, and a survey of related new results, will be of interest to all people interested in discrete geometry, and particularly to young researchers in search of exciting open problems to think about.