
Introduction.- Basics of Manifolds.- Vector Bundles.- Vectors and Covectors.- Differential Forms.- Lie Derivatives.- Lie Groups.- Frobenius Theorem.- Principle Bundles.- Connections on Principle Bundles.- Curvature of a Connection.- Classical Electromagnetism.- Yang-Mills...

This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles. While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics...