A formal scheme is a mathematical concept used in algebraic geometry, particularly in the study of schemes. It provides a way to systematically organize and analyze the properties of algebraic varieties. A formal scheme can be thought of as a generalization of a scheme, allowing for the inclusion of "infinitesimal" structures, which are useful in various applications, such as deformation theory. In a formal scheme, the focus is on rings of formal power series rather than just polynomial rings. This allows mathematicians to work with objects that have a more flexible structure, enabling the study of local properties and behaviors near a point. Formal schemes play a crucial role in modern algebraic geometry and related fields.