This book presents a theory of modeling, analyzing, computing, and optimizing traffic flows on networks. It provides comprehensive and self-contained descriptions and analyses on the widely used conservation law models for dynamic trafic flows on networks. The book covers theoretical aspects of these models using novel and rigorous mathematical techniques, while seeking a balance between theory and practice by including a considerable number of examples and applications. The main topics covered in this books are: First- and high-order conservation law models; Network extensions of fluid-based models; Dynamic network traffic assignment; Control and optimization of traffic flow at urban intersections; Extension of network models to incorporate heterogeneous road conditions; Numerical schemes and computational examples of traffic network models; Applications to traffic sensing,traffic control, and road network design. This book encompasses a wide range of topics in mathematics and engineering and is meant to be a reference and guide to scholars and practitioners. The book also offers materials that support theme-based design of 1-2 semesters of curriculum.