The permanent magnet synchronous motor (PMSM) has become the mainstream choice for automotive traction due to its high torque density and wide speed range. This chapter builds a complete analytical framework for PMSMs. For interior-type machines, the non-uniform air gap produces a salient-pole effect, giving rise to reluctance torque. Based on the four-coil primitive machine model, flux linkage, voltage, and torque equations are derived in the rotor-synchronous DQ frame, where torque naturally separates into excitation and reluctance components. Within the fundamental framework of field-oriented control, the chapter details the maximum torque per ampere (MTPA) trajectory for minimum copper loss in the constant-torque region, the voltage limit ellipse that constrains operation as speed increases, the base speed and transition speed that define the constant-power region, and field-weakening and maximum torque per voltage (MTPV) strategies for extending the speed range beyond base speed.