Connection theory on differentiable fibre bundles. A pedagogical   introduction
  The 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. 
Bozhidar Z. Iliev (Institute for Nuclear Research and Nuclear Energy,   Bulgarian Academy of Sciences, Sofia, Bulgaria)