A Composition Theory for Hexagonal Tilings presents a comprehensive study of composition invariance in hexagonal tilings, expanding foundational work in geometric tiling theory through rigorous mathematical analysis and original research.

Raymond R. Fletcher III introduces a unified framework for understanding λ-polygons and α-polygons, demonstrating how composition invariance extends across a broad class of hexagonally structured polygons. The book develops new theoretical tools, including alternating polygons, derivatives and antiderivatives, dual constructions, and 4-quadrilateral tilings, culminating in new results on strong composition equivalence and the Law of Odd.