SPACE-TIME-MATTERINTRODUCTIONSPACE and time are commonly regarded as the forms of existence of the real world, matter as its substance. A definite portion of matter occupies a definite part of space at a definite moment of timo. It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship. Descartes defined the objective of the exact sciences as consisting in the description of all happening in terms of these three fundamental conceptions, thus referring them to motion. Since the human mind first wakened from slumber, and was allowed to give itself free rein, it has never ceased to feel the profoundly mysterious nature of time-consciousness, of the progression of the world in time,-of Becoming. It is one of those ultimate metaphysical problems which philosophy has striven to elucidate and unravel at every stage of its history. The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew,Table of Contents CONTENTS; PAOI; Introduction j; CHAPTER I; Euclidean Space Its Mathematical Form and its Role in Piiysics § 1 Derivation of the Elomentary Conceptions of Space from that of; Equality ^; § 2 Foundations of AfQne Geometry It; § 3 Conception of n-dimensional Geometry, Linear Algebra, Quadratic; Forms 2J; § 4 Foundations of Metrical Geomotry 21; §5 Tensors 3c; § 6 Tensor Algebra Examplos; § 7 Symmetrica] Properties of Tensors 54; §8 Tensor Analysis Stresses 5£; § 9 The Stationary Electromagnetic Field 64; CHAPTER II; The Metrical Continuum; § 10 Note on Non-Euclidoan Geometry Ti; % 11 Riemann's Geometry 84; § 12 Riemann's Geometry (continued) Dynamical View of Metrics 9£; § 13 Tensors and Tcnsor-donsitiea in an Arbitrary Manifold 102; §14, Affinoly Connected Manifolds 112; §15 Curvature 117; §16 Metr