In this paper a self-contained unitary geometric development of the methods and structures on which the gauge theories are based is developed. This geometrical framework is useful for a more clear understanding of continuum physics. Since the framework is sufficiently generalized, it can be applied to all the situations of physical interest. Contents: Functors and fibre bundles. Derivative spaces and differential equations. Derivative spaces and variational calculus. Connections and derivative spaces. Geometrodynamics of gauge continuum systems and symmetries properties. Classification of gauge continuum systems. Spinor superbundles of geometric objects and dynamics.