This dissertation studies Mach's world-elements and his reduction of space and time to unextended intensities. The elements included not just human sensations, but mind-independent physical qualities in matter. Influenced by J. F. Herbart, Bernhard Riemann and Hermann von Helmholtz, Mach strove to develop a construction of space from these qualities. The study follows these ideas from Mach's intellectual struggles of the 1860s to his late writings, and relies upon extensive extracts from his scientific notebooks and other original documents.