This work gives insight into the philosophical influence Ernst Mach (1838--1916) has had on leading Viennese physicists and philosophers of his time by relating the ideas and works of these men to Mach's phenomenalism. The relation between Mach and the University of Vienna Philosophical Society is also examined. In the process little-known documents and correspondence from Mach are presented. Additionally, this extensive research helps clarify the conflict between Mach and most physicists over the reality of atoms and places the claim of Mach and his followers to represent science and philosophy of science against the claim of Planck and Einstein that phenomenalism and positivism were not even compatible with science. Audience: This is an ideal book for both graduate students and scholars in the field of history and philosophy of science.