Explore the advanced mathematical concepts of C*-algebras in relation to classical and quantum groupoids in this comprehensive lecture. Delve into topics such as localisation, existence, technical aspects, source maps, multipliers, and their properties. Gain insights from Byung-Jay Kahng of Canisius College, USA, as he presents the third part of this in-depth series, offering a rigorous examination of these complex algebraic structures and their applications in quantum theory.