Membranes are essential components in energy-efficient industrial separations (e.g., reverse osmosis, ultrafiltration, gas separations, electrodialysis) and electrochemical devices (e.g., electrolyzers, fuel cells, batteries). This course focuses on the fundamentals of membrane science, as relevant for industrial separations and electrochemical devices. Electrolyte systems are relatively emphasized. The course discusses transport of solvents (e.g., water), solutes, and ions in membranes; polymer chemistry, membrane synthesis, and membrane morphology; and details and requirements of specific applications. The course is relevant for water treatment, mining and metals, chemical processing, and electrochemical engineering.