Translator This monograph develops the Self-Reflexive Monoid Algebra (SRMA), a framework that generalizes the Reflexive Monoid Algebra (RMA) to describe how scientific and cognitive domains can be represented as self-evaluating systems.SRMA introduces a self-generation operator Σ that allows each domain to reproduce its own processes of evaluation, measurement, and refinement, linking algebraic structure with empirical interpretation. The work defines the SRMA lawbook across five canonical representation families (Set, Hilb, CPM, Dom, FRP) and shows how diverse scientific fields—physics, biology, cognition, economics, and information systems—emerge as combinations of these families.It also formulates the principles that maintain coherence between domains, providing a systematic way to couple them while preserving internal consistency. SRMA occupies a precise role in the reflexive hierarchyRMA → SRMA → RCA → GRCA,where it functions both as a concrete model of the Reflexive Category Algebra (RCA) and as the algebraic substrate used by the Generalized Reflexive Closure Algebra (GRCA) to connect theoretical form and empirical observation under the principle of finite reflexive coherence.