Fluvial morphology may be defined as the science of the forms of river‐beds, their shapes in plan and in profile. There seems to be no satisfactory explanation of the cause of lateral migration of streams, that is, of the phenomenon of serpentining or meandering; and this is also true of the rhythm of change of the profile as seen in the downstream‐progression of its pools and concomitant shoals. Extant knowledge is generally qualitative; if quantitative, it is usually of empiric origin and applicable.only to a particular stream. Still there are some universal quantitative principles of fluvial morphology that have been developed theoretically. The purpose of this paper is to present, first, a very brief statement of some of the qualitative observations and, second, a more detailed statement of several quantitative laws and their use.