Fluid interfaces---either between two liquids or between a liquid and a gas---are pervasive in nature and play a crucial role in a wide range of industrial applications. Numerous dynamic processes occur at fluid interfaces, including droplet and spray impact, evaporation, bubble motion, bubbly flows, and foam drainage. In many of these situations, the fluids are multicomponent systems - containing suspended particles or macromolecules that modify their mechanical properties. Likewise, the interfaces they encounter are often complex, being deformable, structured, or otherwise deviating significantly from flat, smooth surfaces. While both complex fluids in their bulk form and the interfacial dynamics of simple fluids have been well studied, the behaviors of complex fluid interfaces are far from fully understood. Several striking examples illustrate the rich dynamics of complex fluid interfaces: (1) the addition of a small amount of polymer can dramatically alter the impact and spreading behavior of liquid drops; (2) mobile surfactants generate surface tension gradients on the surfaces of evaporating drops, driving strong flows and modifying evaporation; and (3) particles can assemble at liquid interfaces to form stable rafts with elastic properties --- hydrophobic liquid marbles exhibit extreme mobility and behave like `dry water'. This summer school will delve into the topic of complex interfaces, with a focus on drops and bubbles. Our goal is to reveal the underlying physical principles and explore engineering applications of fluid interfaces that extend beyond Newtonian fluids and simplified scenarios. This multifaceted field is unified by the physics of free-surface flows, which underpin the rich and diverse interfacial phenomena.
