What are the foundational theories underpinning chemical engineering, encompassing principles of thermodynamics, transport phenomena, reaction kinetics, and process control? How do these theoretical frameworks enable the design and optimization of chemical processes, from unit operations to full$-$scale industrial plants? In what ways do concepts like mass and energy balances, phase equilibria, and fluid dynamics shape the development of innovative technologies for chemical synthesis, separation, and purification? Understanding these theoretical bases empowers chemical engineers to address complex challenges in areas ranging from pharmaceuticals to renewable energy.