Sheaf theory is a mathematical framework used to study how local data can be consistently combined to form global information. It provides a way to organize and analyze data that varies across different spaces, such as in topology or algebraic geometry. A sheaf assigns a set of data to each open set in a space, ensuring that this data behaves well under restriction to smaller sets. In sheaf theory, the concept of "gluing" is essential. If local data on overlapping open sets agrees, it can be combined to create a coherent global section. This idea is crucial in various fields, including cohomology and category theory, where understanding the relationships between local and global properties is fundamental.