In the past two decades numerous laboratories have microfabricated surfaces with the chemical and textural properties to mimic superhydrophobic surfaces (SHs) found in nature, the most well-known being the self-cleaning properties of the lotus leaf. This has been made possible by the continuing advances in nano/micro fabrication technology. This Advanced School will bring together engineers, physicists, chemists and applied mathematicians in a multi-physics framework. Adopting a holistic approach coupling momentum, heat, mass and charge transport phenomena the lecturers comprise 2 applied mathematicians, 2 mechanical engineers, a physicist and a chemist: together they bring theoretical and experimental perspectives to the topic. The fundamentals of the physical and chemical phenomena exploited to suspend liquids in the Cassie (unwetted) state on SHs will be covered. We address the conditions required, and technologies developed, to maintain the Cassie state and those which cause transition to the (sometimes desirable) Wenzel (wetted) state. Transport phenomena physics related to droplets on SHs and flows of liquids over them will be emphasized. For droplets on SHs, the fundamental microfabrication principles including those based on polymer processing technology will be surveyed. Ice prevention and enhancing boiling and condensation heat transfer will be points of emphasis, as will electrowettability-based dynamic control and enhancement of general phase change phenomena. Various approaches to suppress or exploit Leidenfrost phenomena to, e.g., suppress critical heat flux or pump droplets, will be studied. SHs with multifunctional properties such as photo-catalytic activity, anti-reflectivity, abrasion resistance and antisoiling characteristics will be treated. In studying external/internal flows over SHs, the course will include a rigorous derivation of the governing equations and boundary conditions, resolution of surfactant, Marangoni, thermocapillary and molecular phenomena and possible meniscus deformations. Comparison of theoretical models to experiments will be made with implications for key engineering parameters. The course is suitable for graduate students, academics, engineers in industry. The techniques used will span mathematical modelling ideas and numerical schemes, through to experimental procedures and understanding the fundamental physical principles. Applications will be emphasised throughout.