Many things have properties that depend on their shape, such as the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function with respect to a 'shape variable'. This approach, useful for understanding mathematical models containing geometric PDEs, allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute geometric sensitivities by developing basic calculus on surfaces alongside...