2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152282In this paper we consider symplectic and contact Lie algebras. We define contactization and symplectization procedures and describe its main properties. We also give classification of such algebras in dimensions 3 and 4. The classification in dimension~4 is closely connected with normal forms of nondegenerate elliptic equations of the second order on two-dimensional surfaces with transitive symmetry group in first jets. We point out this connection and discuss normal forms.25 pages, LaTexDifferential Geometrytext