Scholz starts his lecture with explaining Weyl geometric scaling; this is used to rescale the metric by a point-dependent factor. This rescaling can be understood by a change of the scale-gauge, giving rise to integrable Weyl geometry (IWG). The IWG is an interesting concept as it is a metrical structure, and provides a link between field theories and gravity. Scholz follows with a discussion of the scale covariance of Einstein and Klein-Gordon equations, and the energy-momentum tensor of a scalar field. The last part of the lecture covers cosmic geometry and a discussion of the Robertson-Walker metric in the context of IWG. The Weyl universe is the simplest scale covariant cosmological model.