2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50936Plan of this report is given below: 1. Motivation from Physical and Mathematical Point of View; 2. Differential Calculi on Finite Groups; 3. Metrics; 4. Lagrangian Field Theory and Symplectic Structure; 5. Scalar Field Theory and Spectral of Finite Groups.LaTeX, 15 pages, with amssymb.sty; no figures or tables. Based on the report on the Seminar "Field Theory, Gravity and Symplectic Structure" [China Center of Advanced Science and Technology (CCAST) & World Laboratory (WL), Beijing, July 9th to July 13rd, 2001]High Energy Physics - TheoryMathematical Physicstext