The book presents a thorough theoretical treatment of all aspects of traditional narrow band model methods for radiation transport. The familiar bands consisting of regular and random line arrangement, as well as various hybrid and cluster arrangements, are treated. Closely related methods such as the exponential wide band and k-distribution approaches are also considered. Particular attention is given to optical paths with exponential-pressure variation (relevant to meteorological applications) and to optical paths consisting of two or more uniform cells in series (relevant to remote sensing applications).