2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73065The (parallel) linear transports along paths in vector bundles are axiomatically described. Their general form and certain properties are found. It is shown that these transports are locally (i.e. along every fixed path) always Euclidean ones in a senses that there exist frames in which their matrices are unit. The investigated transports along paths are described in terms of their local coefficients, as well as in terms of derivations along paths.14 LaTeX pages. For related papers, visit the "publication" pages at http://theo.inrne.bas.bg/~bozho/Differential GeometryGeneral Relativity and Quantum CosmologyMathematical Physics53C99 (Primary) 53B99, 57R35 (Secondary)text