Joseph Liouville was the most important French mathematician in the gen eration between Galois and Hermite. This is reflected in the fact that even today all mathematicians know at least one of the more than six theorems named after him and regularly study Liouville's Journal, as the Journal de Mathematiques pures et appliquees is usually nicknamed after its creator. However, few mathematicians are aware of the astonishing variety of Liou ville's contributions to almost all areas of pure and applied mathematics. The reason is that these contributions have not been studied in their histor ical...