Felix Klein's teaching of Galois theory

This article concerns a lecture course on Galois theory held by Felix Klein in summer 1886 at the University of Göttingen. Klein's commitment to teaching the theory of equations from Galois's advanced point of view forms a remarkable exception within the European curriculum. Klein's heuristic methodology, in which mathematical theory is extracted from a gradually advancing set of examples, allowed him for an efficient introduction of the main principles of Galois theory. At the same time, the lecture was difficult to follow and its immediate success remains questionable. The lecture furthermore provided Klein the possibility to further advertise his so-called Hypergalois vision for algebra, and prepared further lecture courses in that field. Through the commissioned lecture notes and Klein's engagement in the faculty, it also provided the means for a period of stability in the teaching of algebra at the University of Göttingen.