Many things around us have properties that depend on their shape-for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a shape variable. This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts.