This volume presents five different methods recently developed to tackle the large scalebehavior of highly correlated random systems, such as spin glasses, random polymers, local times and loopsoups and random matrices.These methods, presented in a series of lectures delivered within the Jean-Morletinitiative (Spring 2013), play a fundamental role in thecurrent development of probabilitytheoryand statisticalmechanics.The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy...