The various aspects of the Weyl 's geometry has been analysed in this article with the aim to improve the teaching method of geometry in high schools.

It is shown that the Hilbert's infinite-dimensional space, which has a broa(
application in modern Analysis & Theoretical Physics (specially in Quantum
Mechanics) is the result of some modification in one of the Weyl's axioms. It is
further shown that the semi-Euclidean space of Minkowski,which is the mathematical
basis of Einstein's Relativity is also the result of the modification of another axiom of
Weyl's geometry.
The change of the definition of some of the structural elements of 3-dimensional
vector space & 3 - dimensional Euclidean space (such as for example defining
the points as sub-space of a I -dimensional space, the line as sub-space of a 2-dimensional
space, ... ) enables the access to the plane projectif geometry and plane nonEuclidean
Riemann-Lobachevski's geometry.
Finally with due consideration to the Weyl's scientific point of view at
through the study of the adaptation of the Weyl's geometry to the future of scientif
demands it has become evident that his geometry shall replace, sooner or later,
other existing geometries.