It is arguable that most of chemistry and a large portion of atomic physics is concemed with the behaviour of the 92 naturally occurring elements in each of 3 charge states (+1, 0, -1); 276 distinct species. The world of multiply and highly charged ions provides a further 4186 species for us to study. Over 15 times as many! It is the nature of human beings to explore the unknown. This nature is par ticularly strong in physicists although this may not be readily apparent because theses explorations are undertaken in somewhat abstract \'spaces\'. It is, then, no surprise that we have begun to explore the realm of multiply and highly charged ions. Over the past few decades, a consistent1y high quality body of work has emerged as the fruits of this exploration. This intemationally based subject, pursued in universities and research laboratories worldwide, has ex panded beyond its roots in atomic physics. We now see it embracing elements of surface science, nuclear physics and plasma physics as well as drawing on a wide range of technologies. This speciality offers new tests of some of our most fundamental ideas in physics and simultaneously new medical cures, new ways of fabricating electronic gadgets, a major hope for clean sustainable energy and explanations for astrophysical phenomena. It is both a deeply fundamental and a widely applicable area of investigation. 119 Illustrations, black and white; XXXIV, 389 p. 119 illus.