Arthur Holly Compton was one of the great leaders in physics of the twentieth century. In this volume, Robert S. Shankland, who was once a student of Compton's, has collected and edited the most important of Professor Compton's papers on X-rays--the field of his greatest achievement--and on other related topics. Compton entered the field of X-ray research in 1913 and carried on active work until the 1930s, when he began to specialize in cosmic rays. During the years when Compton was an active leader in X-ray research, he made many notable contributions which are reflected in the papers presented here. He was the first to prove several important optical properties of X-rays, including scattering, complete polarization, and total reflection. He was also the first, with his student R. L. Doan, to use ruled gratings for the production of X-ray spectra. Professor Compton's greatest discovery, for which he was awarded a Nobel Prize in 1927, was the Compton Effect. This was the outgrowth of experiments he had initiated during a year at Cambridge in 1919-20. He did the major portion of these experiments at Washington University in St. Louis during the period 1920-24. His work demonstrated that in the scattering of X-rays by electrons, the radiation behaves like corpuscles, and that the interaction between the X-ray corpuscles and the electrons in the scatter is completely described by the principles of the conservation of energy and momentum for the collisions of particles. In his introduction, Professor Shankland gives a historical account of the papers, narrates Professor Compton's early scientific career, and shows how he arrived at a quantum explanation of the Compton scattering after eliminating all classical explanations.