The Authority Discipline establishes governance engineering as a formal discipline whose engineering object is the calibrated boundary between machine capability and institutional authority. The book introduces governance engineering at its birth, identifies the rupture from which it emerged, and locates it relative to the adjacent fields it extends control theory, institutional design, decision theory, and machine learning safety. From a working creed and five first principles, Burak Oktenli develops the master equation: the Authority Migration Function. The function operates on six structural variables authority, baseline, confidence, trust, escalation, and damping and governs the rate at which decision rights migrate from human institutions to machine systems. Across twelve chapters, the book builds the foundations of the discipline: the Calibrated Boundary as the unit of analysis; AI as the machine substrate (four computational layers) and IA as the institutional substrate (eight institutional artifacts); the Cycle-by-Cycle calibration loop that keeps machine action accountable to institutional authority; and the equation in composition the foundational arc that ties every chapter to a unified analytic structure. The book is written for engineers, policy professionals, and institutional leaders confronting machine-speed decision systems in defense, finance, infrastructure, and healthcare. It assumes mathematical literacy but presumes no prior exposure to autonomous systems literature. Each chapter ends with a calibration exercise that operationalizes its concepts. This is the first textbook of governance engineering. The discipline is new. The stakes are not.