  H. Weyl's proposal of 1918 for generalizing Riemannian geometry by local
scale gauge (later called {\em Weyl geometry}) was motivated by mathematical,
philosophical and physical considerations. It was the starting point of his
unified field theory of electromagnetism and gravity. After getting
disillusioned with this research program and after the rise of a convincing
alternative for the gauge idea by translating it to the phase of wave functions
and spinor fields in quantum mechanics, Weyl no longer considered the original
scale gauge as physically relevant.
  About the middle of the last century the question of conformal and/or local
scale gauge transformation were reconsidered by different authors in high
energy physics (Bopp, Wess, et al.) and, independently, in gravitation theory
(Jordan, Fierz, Brans, Dicke). In this context Weyl geometry attracted new
interest among different groups of physicists (Omote/Utiyama/Kugo,
Dirac/Canuto/Maeder, Ehlers/Pirani/Schild and others), often by hypothesizing a
new scalar field linked to gravity and/or high energy physics. Although not
crowned by immediate success, this ``retake'' of Weyl geometrical methods lives
on and has been extended a century after Weyl's first proposal of his basic
geometrical structure. It finds new interest in present day studies of
elementary particle physics, cosmology, and philosophy of physics.
