==================================================== The classification of endotrivial modules By Jon. F. Carlson The objective will be to discuss the recent classification of endotrivial modules over p-groups. This work was recently completed by Jacques Thevenaz and the speaker. The proof shows how homological methods play a role in group representation theory. The first lecture will be devoted to giving an overview of the problem and its motivation. The second lecture will give a hint of the applications of homological algebra. =======================================================