This is an exposition of the geometrical framework for gauge theories, from the bundle viewpoint. In order to handle properly full covariance for physical fields under spacetime transformations the superbundle of geometric objects is introduced. This leads to an interpretation of a spinor field as a superfield of geometric objects, precisely ensuring full covariance for spinor fields.
Contents: 1. Introduction. 2. Functors and fibre bundles. 3. Derivative spaces and differential equations. 4. Derivative spaces and variational calculus. 5. Connections and derivative spaces. 6. Geometrodynamics of gauge continuum systems and symmetry properties. 7. Classification of gauge continuum sytems. 8. Spinor superbundles of geometric objects and dynamics. 9. Conclusions.
Appendix A: Categories, final and initial objects and related structures. Appendix B: Hamiltonian formulation of Noether theorem. Appendix C: 0- sequences, exact sequences and splittings. Appendix D: Homotopy and covering. Appendix E: Euclidean spaces and related isometry groups. Appendix F: Gauge geometrodynamics vs. physical language.