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Conventional transport theory though uses parameters derived from quantum mechanical principles such as energy gap and effective mass, mostly utilizes classical or semi-classical approach. Contrarily, electrical transport in mesoscopic systems is enriched by a number of exotic phenomena driven by the quantum nature of the charge carriers such as quantum tunneling, quantum Hall effects, conductance quantization, flux-quantization, Aharanov-Bohm effect, single-electron charging, Kondo effect and Josephson effects. This course is aimed at giving a comprehensive introduction to many of these phenomena and equipping the prospective students to understand the physical concept and follow the latest developments in this field. The content and lectures are aimed to cater to the senior undergraduate and graduate students aspiring to do their advanced research in area such as solid-state quantum computing technologies, quantum electrical sensing and metrology. INTENDED AUDIENCE : Final year M.Sc. or integrated BS-MS students and Ph. D studentsPREREQUISITES : Introductory Quantum Mechanics & Introductory Solid State PhysicsINDUSTRIES SUPPORT : IBM, Philips Semiconductor, NTT Japan, SQC Sydney, D-Wave systems