  The Ehlers-Pirani-Schild (EPS) constructive axiomatisation of general
relativity, published in 1972, purports to build up the kinematical structure
of that theory from only axioms which have indubitable empirical content. It
is, therefore, of profound significance both to the epistemology and to the
metaphysics of spacetime theories. This axiomatisation is, however,
self-consciously terse, rendering it difficult to ascertain whether it
succeeds. In this article, we provide a pedagogical walkthrough to the EPS
axiomatisation, filling relevant conceptual and mathematical gaps and rendering
explicit controversial assumptions. There are two companion papers, in which we
discuss the significance of constructive approaches to spacetime structure more
generally (Part II), and (with Emily Adlam) consider extensions of the EPS
axiomatisation towards quantum general relativity based upon quantum mechanical
inputs (Part III).
