"Henceforth space by itself and time by itself shall sink to mere shadows, and only a union of the two shall preserve reality." The prophecy contained in the above-quoted words, spoken by Minkowski at the meeting of German "Naturforscher und Aerzte" at Cologne in 1908, has, however, only been completely fulfilled by Einstein's "Allgemeine Relativitäts-theorie" of 1915, which incorporated gravitation into the union. In the following pages an attempt is made to set forth, without using any technical language, the leading ideas of that theory: I will confine myself to the theory as published by Einstein in November, 1915, which forms a consistent whole, complete in itself; and I will not refer to later developments, which are still more or less tentative, and not necessary for the understanding of the theory. The mathematics used by Einstein is the so-called Absolute Differential Calculus. It is not more difficult or recondite than that used in other branches of theoretical physics, but it is somewhat unfamiliar to most of us, because it is not generally taught in the regular university courses. I will, however, in this essay abstain from using any mathematics at all, at least, I will not be using it openly. It is of course unavoidable to use at least the results of the mathematical reasoning, if not the reasoning itself; but so long as they are not put into formulas they will, it is hoped, not look so formidable to the reader. Referring to the quoted words of Minkowski, we may ask what is meant by "reality." Physical science, like common sense, takes for granted that there is a reality behind the phenomena, which is independent of the person by whom, and the particular methods by which it is observed, and which is also there when it is not observed. Strictly speaking, all talk about what is not observed is metaphysics. Nevertheless the physicist unhesitatingly believes that his laws are general, and that the phenomena continue to happen according to them when nobody is looking. And since it would be impossible to prove that they did not, he is fully entitled to his belief. The observed phenomena are the effects of the action of this reality, of which we assume the existence, on the observer's senses--or apparatus, which are extended and refined sense-organs. The laws governing the phenomena therefore must convey some information regarding this reality. We shall never by any means be able to know anything else about it but just these laws. To all intents and purposes the laws are the reality, if we eliminate from them all that refers to the observer alone. What refers to the reality is called "absolute," and what involves reference to the observer "relative." The elimination of the relative is one of the things the theory of relativity has set out to do. THE EXTERNAL WORLD AND ITS GEOMETRY