2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165865In these lecture notes we discuss recent progress in the rigorous derivation of effective evolution equations for the description of the dynamics of quantum mechanical many-body systems.56 pages, 2 figures. Lecture Notes for the mini-course held at the 2008 CMI Summer School "Evolution Equations" at ETH ZurichMathematical PhysicsAnalysis of PDEs35Q55; 81Q15; 81T18; 81V70text