The purpose of this publication is to present (1) faunal lists of the Paleozoic corals of the world arranged in stratigraphic order, and (2) descriptions of several families of Ordovician tetracorals. In Part I each citation includes the present accepted generic and specific term, author, and the date with the type and other localities and geologic formations appropriately marked, followed in parentheses by the synonyms (if any) of each species with the same data designated and any additional information. Part II is concerned with the description of Ordovician genera and species of Tetracoralla which it is believed exhibit the trends of evolution of the corals in general. In comparison these early corals have received much less attention by students than most of the succeeding Paleozoic faunas.