THE philosopher Kant declared that Euclidean geometry was inherent in the human mind and expressed the truth about space. We now recognize that non-Euclidean geometry is equally valid as an abstract system, and that one particular form (due to Riemann) has more claim than Euclidean geometry to represent the properties of physical space. The transition from the old point of view to the new has revealed the true nature of geometry, and thence of mathematics in general, and has helped to build up the theory of relativity. Non-Euclidean Geometry By Prof. H. S. M. Coxeter. (Mathematical Expositions, No. 2.) Pp. xv + 281. (Toronto: University of Toronto Press, 1942.) 3.25 dollars.