Explore the fundamental concepts of group rings and their unit groups in this comprehensive lecture by Eric Jespers. Delve into the structure of group rings, examining their definition, properties, and relationship to ring theory. Investigate idempotents and their significance in group ring theory. Analyze the invertible elements of group rings and understand the equivalence of related problems. Learn about the augmentation mapping and its relevance to unit groups. Discover various constructions of units, including unipotent units and Bass units. Examine the connection between group rings and number theory, exploring cyclotomic units and related theorems. Gain insights into the applications of group rings in representation theory and their importance in modern algebra.