Liouville's theorem has various meanings, all mathematical results named after Joseph Liouville:
- In complex analysis, see Liouville's theorem (complex analysis).
- In conformal mappings, see Liouville's theorem (conformal mappings).
- In Hamiltonian mechanics, see Liouville's theorem (Hamiltonian).
- In linear differential equations, see Liouville's formula.
- In number theory, the theorem that any Liouville number is transcendental, or the lemma involved on diophantine approximation.
- In differential algebra, a theorem which allows one to determine when a given elementary function has no elementary integral, see Liouville's theorem (differential algebra)
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