CONTENTS I. Introduction................................................................................................................. 5 II. Covariant differentiation in fibre bundles............................................................. 7 III. Connection with the Lie derivation....................................................................... 16 IV. Connections in the bundles of differential objects........................................... 19 V. Definition of the covariant derivative in terms of functional equations........... 23 Appendix. Outline of the theory of prolongations.................................................... 29 1. Invariance equations of geometric object............................................................ 30 2. Bases of linear forms and structure equations of fibre bundles.................... 31 3. Prolongations............................................................................................................ 33 References.................................................................................................................... 36