The average river-channel system tends toward an approximate equilibrium between the channel and water and sediment it transports. Both discharge and sediment load principally depend on the drainage basin. Under equilibrium, the stream channel depth, width, velocity, and suspended sediment load at a given cross-section can be expressed as power functions of discharge and these functions constitute the at-a-station hydraulic geometry (AHG). In a similar vein, stream channel depth, width, flow velocity, and suspended load along the river vary with discharge as simple power functions under the condition that the frequency of discharge at all cross-sections is equal. These functions are similar even for rivers having very different physiography and constitute the theory of downstream hydraulic geometry (DHG). The power functions for both types of hydraulic geometry-at-a-station and downstream-form the Leopold and Maddock (LM) (1953) theory which is discussed in this chapter. The discussion is divided according to the type of geometry. For the same discharge frequency along the river, depth, width, and velocity of flow increase with discharge downstream.