What Foundation for Undergraduate Space Geometry?

In first-level undergraduate Geometry courses worldwide, apart from those in which a direct coordinate approach is understood, the ordinary space (the ambient of solid geometry) is introduced either by directly stipulating that its axiomatic model is given by a 3D Euclidean affine space, in the modern structural sense, or on the basis of high school geometry, basically grounded on Euclid’s Axioms, in which case the fact that it gives an example of a 3D Euclidean affine structure is proved. In the present work after a reasonably accurate, though far from being complete, discussion about the mentioned different attitudes, we propose a concise version of Euclid-Hilbert axioms and a reasonably complete deduction of the consequent 3D Euclidean affine structure in the modern sense. This is done with no essential reference to high-school geometry, and much in the style in which other basic mathematical notions are presented in the undergraduate courses.