In recent years, flows in networks have attracted the interest of many researchers from different areas, such as applied mathematicians, engineers, physicists, and economists. The main reason for this ubiquity is the wide and diverse range of applications, including vehicular traffic, supply chains, blood flow, irrigation channels, data networks, and others. This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, along with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Furthermore, the modeling is complemented by analysis, numerics, control, and optimization of flows in networks. The book will be a valuable resource for every researcher or student interested in the subject.