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 context. In the Dictionary of Scientific Biography 1973, Taton [1973] gave a rather sad but also true picture of the Liouville studies carried out up to that date: The few articles devoted to Liouville contain little biographical data. Thus the principal stages of his life must be reconstructed on the ba- sis of original documentation. There is no exhausti ve list of Liou ville's works, which are dispersed in some 400 publications ...His work as a whole has been treated in only two original studies of limited scope those of G. Chrystal and G. Loria.Since this was written, the situation has improved somewhat through the publications of Peiffer, Edwards, Neuenschwander, and myself. Moreover, C. Houzel and I have planned on publishing Liouville's collected works.