This monograph presents the mechanistic foundations of the theory of Morhodynamics, a discipline that investigates the shape of the erodible boundary of natural water bodies. We focus on the fluvial Morphodynamics of straight erodible channels, providing the basis for subsequent extensions to meandering rivers (treated in the companion monograph 2 of this series) and braided rivers. We present basic notions on the Mechanics of Turbulent Flows and Sediment Transport in straight open channels with mobile beds. We then investigate their morphodynamic equilibrium and its instability, that leads to the formation of a variety of bedforms observed in natural rivers. In particular, fluvial bars will deserve special attention as the fundamental building block of large scale fluvial patterns.