This thesis studies the brushless permanent magnet synchronous (BLPM) machine design for electric vehicle (EV) and hybrid electric vehicle (HEV) application. Different rotor topologies design, winding design, and multiphase designs are investigated and discussed. The Nissan Leaf interior permanent magnet (IPM) traction machine has been widely analyzed and there is much public domain data available for the machine. Hence, this machine is chosen as a representative benchmark design. First, the Nissan Leaf machine is analyzed via finite element analysis (FEA) and the results confirmed via published experimental test data. The procedure is then applied to all the following machine designs and results compared. Then the Nissan Leaf machine rotor is redesigned to satisfy the performance specification with sinusoidal phase current in the full range for the same performance specification and permanent magnet material. Afterword, a comparative study assessing the design and performance attributes of the Nissan Leaf IPM machine, when compared to a surface permanent magnet (SPM) machine designed within the main Nissan Leaf machine dimensional constraints. The study illustrates and concludes that both the IPM and SPM topologies have very similar capabilities with only subtle differences between the design options. The results highlight interesting manufacturing options and materials usage. The grain boundary diffusion processed (GBDP) magnets are proposed to reduce the rare earth material content in the permanent magnet machines, especially subject to high load and high temperature operating scenarios by preventing or reducing the onset of demagnetization. The design and analysis procedure of BLPM machine with GBDP magnets are put forward. In the end, the Nissan Leaf IPM machine is taken as an example to verify the analysis procedure. and the results illustrates that IPM machines with GBDP magnets can realize torque and maintain efficiency at high loads while being less prone to demagnetization. A new multi-phase synchronous reluctance machine (SRM) with good torque performance and conventional voltage source inverter is introduced for traction machine applications. Although the torque density is low compared with BLPM machine, the SRM machine gets rid of permanent magnets and achieve low torque ripple compared with switched reluctance machine when the asymmetric inverter is replaced with conventional voltage source inverter. The concentrated windings are designed and studied with both IPM and SPM rotor according to the Nissan Leaf machine requirements of performance and dimension to investigate how the concentrated windings affect the machine performance and manufacturability and cost. 9-, 12-, 15- slot concentrated windings’ stator share the same slot area with the Nissan Leaf machine distributed winding and the performance are evaluated and compared. Multi-phase concentrated windings machines with IPM and SPM rotor are designed and analyzed based on the Nissan Leaf machine specification and dimension constraints. The performance of 23-phase, 5-phase, 9-phase machine at low speed and top speed are studied and the advantages and disadvantages are compared in terms of torque quality, efficiency, and power electronic requirements. / Thesis / Doctor of Philosophy (PhD)