This paper proposes Nestology, a formal analytical framework for the underlying architecture of Artificial General Intelligence (AGI). It defines core concepts (system, parent/subsystem, rules/strategies), deduces five axioms, and derives nine theorems. The core insight is that AGI architectures exhibit a finitely nested structure of “logical non-containment—rule containment,” and subsystems possess dual attributes: absolute rule dependence and relative independence of four elements. Nestology uniquely addresses four core AGI problems: explaining black-box opacity via a quantitative model of cognitive distortion; elucidating emergence through subsystem strategy games; and providing safety-control pathways through rule constriction regulation and cross-level random inspection. The framework’s explanatory power is demonstrated through real-world AGI cases, and comparative analysis shows it complements existing theories. Its applicable scope covers artificially nested architectures with clear hierarchies and controllable rules (e.g., large model–plugin systems). Nestology provides a structured theoretical foundation for recursive self-improvement, value alignment, and safe, controllable AGI development—an essential step toward trustworthy superintelligence.