Although the geometry background from Chapter 3 to the early part of Chapter 6 is self-contained, we attach this appendix to make contact with the more modern language of differential geometry. Fiber bundles can be seen as an obvious generalization of (co-)tangent bundles and allow us to introduce the notion of connections and curvatures in a more invariant manner via the principal bundle. This, in turn, leads to the frame bundle and the spinor bundle, which were implicitly invoked in Chapter 5. A quick overview of G-structure and holonomy classification is followed by how one must deal with spinors in curved spacetime. Although this last part is not used in this volume, it would become an essential tool in the companion book “Geometric Quantum Field Theories.”