For any discussion of the foundations of the Theory of Relativity it seems not only natural but also necessary to look at the art of building foundations itself. I also think that building foundations means constructing an axiomatic physical theory.
Certainly such a view doesn't come as a surprise! However, it seems to me that it has been a bit neglected since 1900 when D. Hilbert pointed out, as his 23rd problem, the need "to treat those physical sciences, in which mathematics play an important role, by means of axioms, like geometry."
Of course, I mean the need for a strict axiomatic theory with a rigor somewhere between that of Euclid's "Elements" and a modern formal language. This is certainly a rigor quite above that of the usual presentations of special relativity (SR) in textbooks or of formulations such as "SR from only one axiom," etc. [1].
In this axiomatic spirit I'm going to briefly present three matters of the Theory of Physical Geometry, i.e. The Theory of Physical Space and Time.
