This introductory text is the first book about quantum principal bundles and their quantum connections which are natural generalizations to non-commutative geometry of principal bundles and their connections in differential geometry. To make for a more self-contained book there is also much background material on Hopf algebras, (covariant) differential calculi, braid groups and compatible conjugation operations. The approach is slow paced and intuitive in order to provide researchers and students in both mathematics and physics ready access to the material.

"The book contains a lot of exercises of different degree of difficulties, but the proofs of the theorems are done in detail. The book is very elaborate and very welcome not only for graduate students, but also for all people interested in mathematical physics." (Stefan Berceanu, zbMATH 1358.58002, 2017)