Abstract : A compilation has been made of numerous topics in the theory of compressible-fluid dynamics. The presentation is designed as a guide for students as well as a source of reference material for the research worker. The choice of material has been influenced by the needs and projects at the Los Alamos Scientific laboratory, where much of the theoretical work in fluid dynamics is carried out by numerical techniques on high-speed electronic computers. There is, however, no discussion of the numerical methods themselves.