This book is on the fundamental studies of electron transport in different 2DEG systems. Electron transport in wide range of GaN samples were studied including in a high carrier density regime where a second conductive subband channel was occupied. The spin-orbit interaction were studied in the GaN heterostructures by using the weak antilocalization measurements. We also studied the energy relaxation processes in the GaN systems to understand the power dissipation. The second topic was electron dynamics on Quantum Hall liquid in GaAs system. We were able to study the Quantum Hall liquids in their deep insulating regime by using single electron transistors. The objective was to understand the charge motions in the quantum Hall liquid in an antidot structure, a particularly important structure for possible device applications in quantum computation. We have also shown that the response associated with the motion of electrons in the bulk of the integer quantum Hall layer could be enhanced by using multiple layers. This finding led us to a magnetometer application which was demonstrated by using a heterostructure with 25 identical multiple quantum wells.