The difficulty in writing a ‘how-to’ book on numerical methods is to find a form which is accessible to people from various scientific backgrounds. When we started this project, hierarchical N-body techniques were deemed to be ‘too new’ for a book. On the other hand, a few minutes browsing in the References will reveal that the scientific output arising from the original papers of Barnes and Hut (1986) and Greengard and Rohklin (1987) is impressive but largely confined to two or three specialist fields. To us, this suggests that it is about time these techniques became better known in other fields where N-body problems thrive, not least in our own field of computational plasma physics. This book is therefore an attempt to gather everything hierarchical under one roof, and then to indicate how and where tree methods might be used in the reader's own research field. Inevitably, this has resulted in something of a pot-pourri of techniques and applications, but we hope there is enough here to satisfy the beginners and connoisseurs alike.