2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149748We classify simple flops on smooth threefolds, or equivalently, Gorenstein threefold singularities with irreducible small resolution. There are only six families of such singularities, distinguished by Koll{á}r's {\em length} invariant. The method is to apply invariant theory to Pinkham's construction of small resolutions. As a by-product, generators of the ring of invariants are given for the standard action of the Weyl group of each of the irreducible root systems.73 pages, AMSLaTeX v1.1Algebraic Geometrytext