Sheaf Theory is a branch of mathematics that studies how local data can be collected and related to form global information. It provides a framework for understanding how different pieces of information, defined on various open sets of a space, can be glued together to create a coherent whole. This is particularly useful in areas like algebraic geometry and topology. In Sheaf Theory, a sheaf consists of a set of sections that can be assigned to open sets in a topological space. These sections must satisfy certain conditions, such as being compatible on overlaps of open sets. This concept helps mathematicians analyze complex structures by focusing on local properties and their interactions, making it a powerful tool in modern mathematics.