The Austrian scientist Ernst Mach (1838-1916) carried out work of importance in many fields of enquiry, including physics, physiology, psychology and philosophy. Published in this English translation of 1906, these essays examine geometry from three different perspectives. Mach argues that, as our ideas about space are created by the senses and how we experience our environment, researchers must not consider the subject from a mathematical standpoint alone. In the first essay, he explains how humans generate spatial concepts. Next, he discusses the psychology of geometry, its empirical origins, and its development. In the final piece, he writes from the viewpoint of a physicist, outlining how various mathematicians, such as Carl Friedrich Gauss and Bernhard Riemann, have contributed to our geometrical understanding. Also reissued in this series in English translation are Mach’s The Science of Mechanics (1893) and Popular Scientific Lectures (1895).