This fourth and final volume of The Collected Papers of Sir William Rowan Hamilton (1805–1865) contains three previously unpublished and important manuscripts, namely Systems of Rays and two lengthy letters to de Morgan (on definite integrals) and Hart (on anharmonic coordinates). In addition the volume contains reprinted papers on geometry, analysis, astronomy, probability and finite differences, as well as a collection of papers on various topics. A cumulative index for all four volumes is provided, as well as a CD containing all four volumes of the Collected Papers.