Deformation of algebras and modules (Ch. Geiss) ----------------------------------------------- 1) Schemes of modules and algebras; interpretation of tangential spaces as Ext^1_A(M,M) resp. as H^2(A,A). 2) Infinitesimal and formal deformations of modules and algebras; interpretation of obstructions via Ext^2_A(M,M) resp. H^3(A,A). dg-Lie algebra structures on Ext^* and H^*. 3) Applications: A local criterion for smoothness, decomposition theory for module varietes after Crawley-Boevey and Schroeer. 4) Degenerations of modules and algebreas: An overview of fundamental results, examples and problems.