2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208186The relationship (both classical and quantum mechanical) between the discrete Liouville equation and Teichmüller theory is reviewed.24 pages, 11 figures, submitted to Handbook in Teichmüller theory, minor corrections, references addedQuantum AlgebraMathematical Physics81R12text