2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103516The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic and arbitrary frames is considered.44 LaTeX pages. The packages AMS-LaTeX and amsfonts are required. v2: minor style changes and correction of misprints. For other papers on the same topic view the "publication" pages at http://theo.inrne.bas.bg/~bozho/Mathematical PhysicsGeneral Relativity and Quantum CosmologyDifferential Geometry53C05, 53B05 (Primary) 58A30 (Secondary)text