Mesoscopic physics and quantum Hall systems provide a compelling intersection of experimental accessibility and deep theoretical insight, making them essential for exploring low-dimensional quantum phenomena. Mesoscopic systems, which exist between the macroscopic and quantum scales, reveal striking quantum effects due to electron confinement in small geometries. This confinement gives rise to discrete energy levels, quantized conductance, and coherence phenomena, offering a crucial bridge between classical and quantum mechanics. A key example of these quantum effects is the Quantum Hall Effect, observed in two-dimensional electron gases subjected to strong magnetic fields. The Quantum Hall effect, characterized by precisely quantized Hall resistance, has not only validated fundamental quantum principles but also revolutionized our understanding of electronic systems through topological concepts. These findings highlight the fundamental role of mesoscopic physics in advancing quantum science and developing future quantum technologies.