The aim of this introductory chapter is to present the scope of this thesis fixing basic notions and terminology, as well to provide a complete, but non technical, exposition of the main results. Section 1.1 is devoted to a historical review of the quantum Hall effect (QHE), trough main steps that lead to its “topological interpretation”. The notions of topological quantization and topological quantum numbers are expounded using
the Dirac’s monopole as a paradigm.....
