The chapter from Hartley Rogers, Jr.'s "Theory of Recursive Functions and Effective Computability" (Volume 1, 1957) introduces the foundational concepts of recursive functions and effective computability. It provides an overview of the theoretical framework that underpins the study of algorithms and computational processes, focusing on the mathematical properties and behaviors of recursive functions. The text is part of a broader exploration of the computational capabilities of algorithms and the limits of what can be computed.The chapter from Hartley Rogers, Jr.'s "Theory of Recursive Functions and Effective Computability" (Volume 1, 1957) introduces the foundational concepts of recursive functions and effective computability. It provides an overview of the theoretical framework that underpins the study of algorithms and computational processes, focusing on the mathematical properties and behaviors of recursive functions. The text is part of a broader exploration of the computational capabilities of algorithms and the limits of what can be computed.