The spin-orbit(SO) interaction has widely applied in proposals of spintronic devices. It offers an approach to control the election spin without external magnetic field in semiconductor and metallic nanostructures. The dominant SO couplings which are relevant to planar semiconductor heterostructures are the Rashba and Dresselhaus effects. The former is due to the structure inversion asymmetry(SIA) which can be controlled by gate voltage and the latter is due to the bulk inversion asymmetry(BIA). In this thesis, we study geometrical effects of SO interaction on two-dimensional electrongas(2DEG) system. It is showed the SO coupling including Rashba and Dresselhaus terms can be regarded as a non-Abelian SU(2) gauge field. In chapter two, we survey on some well-known theories in two field of physics; they are spin-orbit coupling thoery and gauge transformation. In chapter three we will use some tricks to maneuvre the gauge transformation in calculation spin precession in spin-orbit field. Extending this method, we can use SO gauge field to calculate the spin transport in a two-dimensional system which is affected by space-dependent SO couplings. In chapter four, we make the summary and give some directions of future work.