2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149168I review the foundations of irrational conformal field theory (ICFT), which includes rational conformal field theory as a small subspace. Highlights of the review include the Virasoro master equation and the generalized Knizhnik-Zamolodchikov equations for the correlators of ICFT on the sphere and the torus.LaTex file, 16 pages, Invited talk at the XIth International Congress of Mathematical Physics, Paris, July 18-23, 1994, One misspelled name correctedHigh Energy Physics - TheoryIrrational Conformal Field Theory on the Sphere and the Torustext