2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110308This paper is an exposition of the representation theory of vertex operator algebras in terms of associative algebras A_n(V) and their bimodules. A new result on the rationality is given. That is, a simple vertex operator algebra V is rational if and only if its Zhu algebra A(V) is a semisimple associative algebra and each irreducible admissible $V$-module is ordinary.13 pages, final version for publicationQuantum AlgebraRepresentation Theory17B69text