Abstract We present a comprehensive overview of the Constructive Gauge Theory Program (CGTP), a three-volume series establishing the rigorous existence of a strictly positive mass gap in pure Yang-Mills theory on ℝ⁴. This document serves as a roadmap to theproofs detailed in the companion volumes, elucidating the logical architecture that connects semiclassical analysis on ℝ³ × S¹ (Volume I) with constructive renormalization group stability (Volume II) and axiomatic spectral reconstruction (Volume III). We explain how the program overcomes historical obstructions—specifically the conflict between infrared slavery and non-perturbative analysis—by utilizing a hybrid strategy that combines adiabatic continuity with Balaban’s ultraviolet stability bounds. We summarize the main result: the construction of a non-trivial Relativistic Quantum Field Theory satisfying the Osterwalder-Schrader axioms and exhibiting a discrete spectrum bounded away from zero.