While working on our common problems, we often used our meetings to dis- cuss also the fundamentals of physics and the implications of new results in mathematics for theoretical physics. Out of these discussions grew the work presented in this monograph. It is an attempt at answering the following ques- tion: What mathematical structures does Einstein–Weyl causality impose on a point-set M that has no other structure defined on it? In order to address this question, we have, first of all, to define what precisely we mean by Einstein- Weyl causality – that is, to provide an axiomatization of this notion. It may be remarked that we were led to the axiomatization given in Chap. 3 by physical intuition, and not by mathematical analogy.