A hypersurface is a generalization of surfaces in higher-dimensional spaces. In mathematics, particularly in geometry, a hypersurface is defined as a subset of a higher-dimensional space that has one less dimension than the space itself. For example, in a three-dimensional space, a hypersurface would be a two-dimensional surface, like a sphere or a plane. Hypersurfaces are important in various fields, including algebraic geometry and differential geometry. They can be described by equations, and their properties are studied to understand the structure of the surrounding space. In physics, hypersurfaces can represent boundaries or interfaces in theories such as general relativity.