An alluvial river is a river in which the bed and banks are made of mobile sediment. Alluvial rivers are self-formed, meaning that their shape result from the feedback between flow dynamics and sediment transport. As a result, rivers build their own bed, selecting both their width and slope and developing planforms that can be meandering, or braiding. At a larger scale, rivers organize into a dendritical network called the drainage network. In this lecture, we will discuss some aspects of the interaction between flow and sediment transport with the goal to understand how a mechanism which operates at the scale of the fluid-grain interaction (typically the centimeter and the second) selects the shape of alluvial rivers and controls the growth of the drainage network. In the second part of the lecture we will use recent publications on the flux of matter and dissolved elements to discuss the concept introduced in the first part of the lecture. The focus will be on the amazon basin and its different watershed of different sizes. The objectives are to discuss the selection of papers. Groups of 2 PhD candidate will make first a short presentation of the papers to be discussed. The lecture should be critical and raise issues to be addressed in the futur. The outcome of this work could be the the redaction of a research proposal (2 pages) on identified topics.