2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142068In this paper a concise, complete proof of resolution of singularities of 3-folds in positive characteristic (>5) is given. The first proof of this theorem was given by Abhyankar in 1966. The resolution morphism in our proof is an isomorphism over the nonsingular locus.55 pages. In this final version, which is to appear in the American Journal of Mathematics, complete details of the proof of embedded resolution of surfaces have been added in. Two sections have been added after the introduction, giving an outline of the proof, and discussing related results and extensions of the material proved in this paperAlgebraic GeometryCommutative Algebra14J17text