Transportation engineering encompasses a wide array of theoretical frameworks aimed at optimizing the efficiency and safety of transportation systems. Expound upon the principles of traffic flow theory and its relevance in the design and management of transportation networks. Analyze the fundamental characteristics of traffic flow, including density, speed, and flow rate, and elucidate the mathematical models used to describe and predict traffic behavior under different scenarios. Additionally, investigate contemporary challenges in transportation engineering, such as urban congestion, sustainability, and the integration of emerging technologies like autonomous vehicles and intelligent transportation systems $($ITS$),$ and propose theoretical approaches to address these multifaceted issues while ensuring the seamless movement of people and goods.