I am looking for references about connections on a generic fiber bundle. A lot of books deal with connections on vector bundles, some books as the Kobayashi-Nomizu generalize the concept of connection to principal bundles. I know that exists also a more general notion of connection on fiber bundles (for example in Kolar-Michor-Slovak's book "Natural Operators in Differential Geometry" it is shown using horizontal and vertical bundles), but I have had some difficulties in finding other good references.
Can someone suggest me a good book?
This question is different from Reference Request for Fibre Bundle Theory from the Smooth Manifold Point of View as mine it is more specific on connections, among the books suggested there only the abovementioned K-M-S deals with connections on general fiber bundles.