2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143724We study the tropical lines contained in smooth tropical surfaces in R^3. On smooth tropical quadric surfaces we find two one-dimensional families of tropical lines, like in classical algebraic geometry. Unlike the classical case, however, there exist smooth tropical surfaces of any degree with infinitely many tropical lines.27 pages, 12 figures. v2: Errors corrected, notation improved, referances added, Example 9.3 newAlgebraic GeometryCombinatoricstext