Liouville left more than 340 notebooks, consisting of more than 40,000 pages in which he examined a great variety of topics. The author has spent years studying that material, and has produced a perfectly marvelous scientific biography. In Part I (six chapters) he recounts the outward events of Liouville's life and career. In Part II (which with its appendices runs to more than 500 pages) he reviews serially (and brilliantly) Liouville's diverse contributions to physics and to mathematics (exclusive of his contributions to number theory). Both Lutzen and his publisher are to be complemented for a splendid accomplishment, the production of a book which belongs absolutely in every mathematical library, and which will be consulted/read with admiring pleasure by generations of Liouville's successors.