Explore the fundamentals of integer quantum Hall effect in this comprehensive lecture by Ganpathy Murthy at the International Centre for Theoretical Sciences. Delve into topics such as the classical Hall effect, clean non-interacting Hamiltonian, Landau gauge, and gauge arguments by Laughlin and Halperin. Examine key concepts including degeneracy, charge passing, Faraday EMF, and conductivity equations. Gain insights into the latest research on topological phases of matter, edge dynamics, and their applications in condensed matter physics. Suitable for senior PhD students, postdocs, and faculty working in related areas, this lecture provides both a pedagogical introduction and an overview of recent developments in the field.