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
  • 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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