The main purpose in this thesis is to investigate spin transport characteristics of two- and three-terminal Aharonov-Cashser (AC) quantum rings under different spin-orbit interaction (SOI) strength. Reflection and transmission analysis completed by using one-dimensional quantum waveguide theory and transfer matrix. Via selecting ap-propriate radius of ring and electric field, the two-terminal ring structure can be used as a series of quantum gates on specific angle of the leads, including phase-shift gate, Pau-li- gate, Pauli - gate, Pauli- gate, and Hadamard gate. In the innovative part, the complete analytical solution of these gates is proposed in this study, and amounts of rings applied in quantum gates are more optimized than previous studies. Three-terminal AC rings can make unpolarized incoming electrons become to fully polarized spin states with different directions at two output leads, which is the main key of this paper. At the same time, the influence of the three-terminal AC rings with different angle of leads on spin polarization and reflectionless is also discussed. In addition, the device can be used to realize quantum walk in the combination with the two- and three-terminal AC rings, providing a scheme of solid-state device.