2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73058We give a proof of, for the case of contact structures defined by global contact 1-forms, a Theorem stated by Eliashberg that for any overtwisted contact structure on a closed 3-manifold, its contact homology is 0. A different proof is also outlined in the appendix by Yakov Eliashberg.17 pages. Typos corrected. One reference updatedSymplectic GeometryDifferential Geometry57R17, 57R65, 53DXX, 58C10text