Reference for principal bundles and related concepts

Question

I am looking for a good reference for fibre bundles on differential manifolds, Ehresmann connections, principal $G$-bundles and principal Ehresmann connections (the $G$-equivariant version of Ehresmann connections). Could anyone advise me on this? I have looked at the book Fibre Bundles by Hausmöller, but it isn't quite what I want.

Thanks in advance.

Answer 1

I can suggest:

• Kobayashi S., Nomizu K. - Foundations of Differential Geometry; Volume 1, Chapter 2 and Note 1; Volume 2, Chapter 9, Subsection 3 and Note 12.
• Kolář I., Michor P. W., Slovák J. - Natural Operations in Differential Geometry, Chapters 3 and 4;
• Spivak M. - A comprehensive introduction to differential geometry, Volume II, Chapter 8;

where only the third book is easy and intuitive.