Topos theory is a branch of mathematics that generalizes set theory and category theory. It provides a framework for understanding mathematical structures through the concept of a topos, which is a category that behaves like the category of sets. This allows mathematicians to study properties of spaces and functions in a more abstract way. In topos theory, each topos can be thought of as a universe of sets, where logical operations and set-theoretic concepts can be applied. This theory has applications in various fields, including logic, geometry, and theoretical computer science, enabling deeper insights into the foundations of mathematics.