2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141845We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its rank is not too large, while semistable torsion-free sheaves satisfying certain cohomological conditions are instanton. We also study a few examples of moduli spaces of instanton sheaves.31 pages. V2: Completely reformulated, errors corrected. V3: misprints corrected, few remarks added. V4: more misprints corrected, few remarks added.V5: final version to be published at Collectanea MathematicaAlgebraic Geometry14j60; 14f05text