Stephen Bruce Sontz is a Professor at Centro de Investigacion en Matematicas (CIMAT). He received his Ph.D. from the University of Virginia, USA, in 1994.

"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)

• Introduction.- First Order Differential Calculus.- Fodc's of a Hopf Algebra.- Adjoint Co-action.- Covariant Bimodules.- Covariant Fodc's.- The Braid Groups.- An Interlude: Some Abstract Nonsense.- The Braided Exterior Algebra.- Higher Order Differential Calculus.- Structures.- Quantum Principal Bundles.- Finite Classical Groups.- Dunkl Operators as Covariant Derivatives in a QPB.- What Next?.