Type theory is a branch of mathematical logic and computer science that focuses on classifying entities into different categories, or "types." Each type defines a set of values and the operations that can be performed on them. This helps prevent errors in programming by ensuring that operations are applied to compatible data types, enhancing both safety and clarity in code. In type theory, types can be simple, like integers or booleans, or more complex, such as functions or data structures. It serves as a foundation for various programming languages and systems, including Haskell, ML, and Coq, which utilize type systems to enforce rules and improve reliability.