Differential forms are mathematical objects used in calculus and geometry to generalize the concept of functions and integrals. They allow for the integration of functions over various dimensions, such as curves, surfaces, and higher-dimensional spaces. This framework is particularly useful in fields like physics, engineering, and differential geometry. A differential form can be thought of as a way to encode information about how quantities change in space. They are often represented using symbols like \omega and can be manipulated using operations such as exterior differentiation and wedge products. This makes them powerful tools for expressing physical laws, such as Maxwell's equations in electromagnetism.