Magneto-transport study on high mobility electron systems in both 2D- and 3D- case has attracted intense attention in past decades. This thesis focuses on the magnetoresistance behavior in 3D topological insulator Bi2Te3 and GaAs/AlGaAs 2D electron system at low magnetic field range 0.4T the first drop at T~3.4K to tndium superconductor and considered the second drop at lower temperature as the proximity effect that occurred near the interface between these two materials. On the other hand, GaAs/AlGaAs heterostructure, as a III-V semiconductor family, has been extensively studied for exploring many interesting phenomena due to the extremely high electron mobility up to 10^7 cm^2/Vs. In this thesis, two interesting phenomena are present and discussed in a GaAs/AlGaAs system, which are the electron heating induced tunable giant magnetoresistance study and phase inversion in Shubnikov-de Haas oscillation study, respectively. By applying elevated supplementary dc current bias, we found a tunable giant magnetoresistance phenomenon which is progressively changed from positive to giant negative magnetoresistance. The observed giant magnetoresistance is successfully simulated with a two-term Drude model at all different dc biases, I_{dc}, and temperature, T. In addition, as increasing the dc current bias, a phase inversion behavior was observed in Shubnikov-de Haas oscillation, which was further demonstrated by the simulation with an exponential damped cosine function. This thesis also presents an ongoing project, which is the observation and fabrication of 2D layered materials. The studied 2D layered materials includes graphene, biron nitride, Molybdenum disulfide, etc. At the end, a future work about fabrication of the 2D layered materials devices as well as the suggestion about the measurement are discussed.