This volume is edited as the proceedings of the 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) 'The Role of Metrics in the Theory of Partial Differential Equations', held for the period of July 2-13, 2018 in Hokkaido University, Sapporo, Japan. This volume consists of peer-reviewed articles written by speakers who actively lead the fields of partial differential equations, numerical analysis, harmonic analysis, and geometric analysis. It should be underlined that 3 survey articles provided by course lecturers show an interesting direction of analysis under various metrics. This volume is suitable for any graduate students and young researchers to motivate the research on these fields from the viewpoint of metrics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America