The author gives a short account of the L-concept which has been developed by G. Ludwig [Die Grundstrukturen einer physikalischen Theorie, Springer-Verlag (1978; Zbl 0387.00010)] for the description of physical theories and which includes as a particular component a mathematical theory in the sense of N. Bourbaki [Elements of mathematics. Theory of sets, Paris (1968; Zbl 0175.270)]. Within this methodological framework a space-time theory is developed starting with rather primitive notions. This is done by a stepwise extension of a preliminary theory where events, signals and other elementary objects are studied. In this context every set of axioms is preceded by intuitive descriptions before the precise formulations are written down.
The subjects which lead to the first and second extensions of the preliminary theory are clocks and light signals. In this framework causal structures and light rays are investigated. Also some topological considerations are exhibited on this base. The next extension introduces special requirements for the distributions of light rays. In this context radar coordinates can be introduced. But the framework is not sufficient to derive the manifold structure of space-time under these general conditions. To this purpose additional assumptions will have to be made which are to appear in the second part of the paper under consideration.