I. The Career of a Mathematician -- I. Youth (1809–1830) -- II. Climbing the Academic Ladder (1830–1840) -- III. Professor, Academician, and Editor (1840–1848) -- IV. The Second Republic (1848–1852) -- V. The Last Flash of Genius (1852–1862) -- VI. Old Age (1862–1882) -- II. Mathematical Work -- VII. Juvenile Work -- VIII. Differentiation of Arbitrary Order -- IX. Integration in Finite Terms -- X. Sturm-Liouville Theory -- XI. Figures of Equilibrium of a Rotating Mass of Fluid -- XII. Transcendental Numbers -- XIII. Doubly Periodic Functions -- XIV. Galois Theory -- XV. Potential Theory -- XVI. Mechanics -- XVII. Geometry -- Appendix I. Liouville on Ampère’s Force Law -- Appendix II. Liouville’s Notes on Galois Theory -- Notes -- Unpublished Manuscripts and Other Archival Material -- List of J. Liouville’s Published Works -- Other References.