| The quantum Hall effect (QHE) is one of the most remarkable phenomena of nature. Since its discovery in 1980 it has motivated an extensive theoretical and experimental work, which led to the development of many fundamental concepts of the condensed matter physics and gave rise to important practical applications. Nowadays, cleaner samples made it possible to observe the QHE in magnetic fields as low as several tenths of a Tesla. Several new interesting findings have been reported. I investigate this new range of magnetic fields in order to explain these findings and establish the connection with previously studied case of strong magnetic fields. Specifically, I study the effects of localization and electron-electron interactions on thermodynamical and transport properties of the system.; The thesis covers the following topics: the theory of the collapse of the spin-splitting, the study of the ground state structure of a partially filled Landau level, and the theory of the crossover from the Shubnikov oscillations to the QHE in case of a long-range disorder. |
