Just like Augustin-Louis Cauchy before him, Liouville studied engineering at École des Ponts et Chaussées after graduating from the Polytechnique, but opted instead for a career in mathematics.

Liouville founded the Journal de Mathématiques Pures et Appliquées which retains its high reputation up to today, in order to promote other mathematicians' work.

He was the first to read, and to recognize the importance of, the unpublished work of Évariste Galois which appeared in his journal in 1846.

[5] In mathematical physics, Liouville made two fundamental contributions: the Sturm–Liouville theory, which was joint work with Charles François Sturm, and is now a standard procedure to solve certain types of integral equations by developing into eigenfunctions, and the fact (also known as Liouville's theorem) that time evolution is measure preserving for a Hamiltonian system.

In Hamiltonian dynamics, Liouville also introduced the notion of action-angle variables as a description of completely integrable systems.