Eichfeldtheorie

This textbook provides an introduction to differential geometry on fiber bundles. After a chapter on Lie groups and homogeneous spaces, it discusses locally trivial fibrations, particularly principal bundles and the associated vector bundles. The fundamental concepts of differential calculus on fiber bundles are then presented: connection, curvature, parallel transport, and covariant derivative. Following this, the holonomy groups are introduced, which play a central role in differential geometry. Applications such as characteristic classes and the Yang-Mills equation are also covered. Numerous exercises with hints for solutions help to deepen the understanding of the material. The book is primarily aimed at master's students in mathematics and physics. It provides the mathematical foundations needed in lectures on gauge field theory in theoretical and mathematical physics.