Recursion Theory, also known as Computability Theory, is a branch of mathematical logic that studies the properties of computable functions and the limits of what can be computed. It explores the concept of recursive functions, which are functions that can be defined in terms of themselves, allowing for the analysis of algorithms and their effectiveness in solving problems. The theory also examines various classes of problems, such as decidable and undecidable problems, which determine whether a problem can be solved by an algorithm. Key figures in this field include Alan Turing, whose work laid the foundation for understanding computation and the limits of algorithmic processes.