The Grzegorczyk hierarchy is a classification of functions based on their complexity, particularly in the context of computability theory. It organizes functions into levels, where each level represents a different type of computable function. The hierarchy starts with basic functions and progresses to more complex ones, illustrating how certain functions can be built from simpler ones. Each level of the Grzegorczyk hierarchy corresponds to a specific type of recursion, allowing mathematicians to analyze the capabilities of various computational models. This framework helps in understanding the limits of computation and the relationships between different classes of functions, contributing to the broader field of mathematical logic.