A famous problem found in books on mathematical recreations was first proposed in an annual in 1850 by a vicar and amateur mathematician, Thomas Kirkman. Fifteen schoolgirls walk out three abreast for seven days and it was required to arrange each day's walk so that any pair of girls were only once in the same row during the week. The puzzle arose from Kirkman's work on a more general mathematical problem which he was to explore in a number of published articles over the next few years. Much of his work was ignored at the time, but it involved various combinatorial ideas that have now become of some interest and importance. He was also interested in a range of other mathematics, such as the theory of polyhedra, the newly developing theory of groups, and the classification of knots. He was respected by many of his professionals and was elected a Fellow of the Royal Society. This book presents a brief account of the original problem and some of the ways it has been generalised and eventually solved. It also surveys in a not too technical way, some of the other work of a remarkable nineteenth-century polymath.