The usual book on the theory of spectral line formation begins with an in-depth dis cussion of radiation transfer, including the elegant methods of obtaining analytical solutions for special cases, and of the physics of line broadening. Neither of those features will be found in this book. It is assumed that the reader is already familiar with the essentials of transport theory and of line broadening and is ready to investi gate some of the particular applications of the theory to the flow of line photons through the outer layers of a star, or other tenuous media. The main thrust of this book is toward the compilation and presentation of a vast quantity of computational material available to the author in the form of computer output. The material presented represents a highly filtered sample of the published work in this subject plus an extensive set of previously unpublished results. To present large quantities of computer output in an intelligible and efficient way is a difficult task, for which I have found no really satisfactory solution. Chapters III and IV, in particular, contain almost exclusively this type of presentation. The reader may find these chapters somewhat tedious because of the level of condensation of the material. I have tried to reach a reasonable balance between over condensation and excessive detail, which in the long run may be irrelevant.