1. Experimental evidence for Drude-Boltzmann transport-like behavior in an AlGaN/GaN two-dimensional electron system We have measured the low-temperature electron transport properties in a AlxGa1−xN/GaN heterostructure. I shall report magnetotransport measurements on an AlGaN/GaN two dimensional electron gas over a wide range of temperature (0.3 K T 80 K). In the low-temperature regime, the magnetoresistivity oscillate as the magnetic field increases. At highest measurement temperature of T = 80 K, i.e., the quasiclassical regime, the longitudinal resistance is nominally magnetic field independent which is ascribed to evidence for Drude-Boltzmann-like transport in a 2D electron system. 2. Experimental Studies of Low-field and High-field Landau Quantization in Two-dimensional Electron Systems in GaAs/AlGaAs Heterostructures In Ando formalism, the assumption is that the background resistivity of 2DEG is constant and unchanged as the magnetic field increases. In our result we found that SdH formula is still valid although the oscillating amplitude becomes larger than the value of xx at B = 0. ii However, the same analysis for composite fermions of = 3/2 is not consistent with Ando formula. The reason may be that at = 3/2 the magnetic field is not enough to transform all the electrons to composite fermions. Therefore the behavior of this system can not be described by pure composite fermions or pure electrons. The effect in this regime should be described by the combinations of composite fermions and electrons.