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This paper proposes a systematic approach for the development of electric machine windings with reduced magnetomotive force (MMF) space harmonic content. By identifying the levels and slot position angles in the winding function of an electric machine winding, the winding factor, the magnitudes of individual harmonic components and thus the MMF spectrum of a winding can be represented mathematically as functions of the levels and angles. With numerical optimization, these functions can act as the constraints and the objective function. A typical formulation is to limit the magnitudes of undesired harmonics and to maximize the winding factor of the working component. The result of the optimization is often a new winding layout with potentially unequally pitched slots and different turns for the coils within a phase, and reduced or even eliminated harmonic orders of design interest, while maintaining a reasonable winding factor. The mathematical representation and design approach is applicable to both distributed windings and fractional-slot concentrated windings (FSCWs), with no special requirements on the slot/pole combination and the number of layers. Two design examples, a mixed-layer distributed winding and a 24-slot, 22-pole double-layer FSCW, are shown to have improved electromagnetic performance with finite element simulations. [ABSTRACT FROM AUTHOR]