This is a partial review of the connection theory on differentiable fibre bundles. From different view points, this theory can be found in many works, like [2–6, 9, 13–15, 18, 19, 24, 26, 27, 30, 31, 35–40, 42]. The presentation of the material in Sections 2–5, containing the grounds of the connection theory, follows some of the main ideas of [30, Chapters 1 and 2], but their realization here i...