Liouville's theorem has various meanings, all mathematical results named after Joseph Liouville:

• In complex analysis, see Liouville's theorem (complex analysis)
  • There is also a related theorem on harmonic functions
• In conformal mappings, see Liouville's theorem (conformal mappings)
• In Hamiltonian mechanics, see Liouville's theorem (Hamiltonian) and Liouville–Arnold theorem
• In linear differential equations, see Liouville's formula
• In transcendence theory and diophantine approximations, the theorem that any Liouville number is transcendental
• In differential algebra, see Liouville's theorem (differential algebra)
• In differential geometry, see Liouville's equation
• In coarse-grained modelling, see Liouville's equation in coarse graining phase space in classical physics and fine graining of states in quantum physics (von Neumann density matrix)