2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107569We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any such Lie algebra is up to isomorphism either classical (i.e. comes from characteristic 0) or a filtered Lie algebra of Cartan type or a Melikian algebra of characteristic 5.Revised version: a list of open problems has been added as suggested by the refereeRings and AlgebrasQuantum Algebra17B20, 17B50text