According to the most popular interpretation of A. Einstein’s relativity theories, they imply elimination of the ether and a deep revision of the notions of motion, space and time. In spite of this, H.A. Lorentz’s dynamical interpretation, adopted in this book, re-introduces the notion of the ether, both as the bearer of fields of fundamental interactions (material ether) and as a distinguished reference frame (geometrical ether), along with the absolute time and Euclidean background geometry of space. The metaphysical doctrine of radical aristotelism, a slightly liberalized and enriched version of T. Kotarbiński’s reism, provides a part of a deeper conceptual background for it. Another part of this background is supplied by P. Lorenzen’s protophysics. It is argued that, whereas some of the above notions are clearly metaphysical, others are protophysical. Protophysics provides strong reasons for introducing some background space-time geometry and conditions which it must satisfy. This application makes prospects for arousing interest in protophysics among specialists in relativistic physics.