The lecture notes of Julian Schwinger’s UCLA course consist of three parts corresponding to the three quarters of teaching. The first part begins with an analysis of Stern–Gerlach-type experiments which accomplishes a self-contained physical and mathematical development of the general structure of quantum kinematics. The second part proceeds from there. The response to infinitesimal time displacements yields the equations of motion. Then the Quantum Action Principle (QAP) is derived, and accepted as a fundamental principle. In a sense, the rest of part two and all of part three consist of instructive applications of the QAP.