The discovery of the Stochastic Loewner Evolution (SLE) by Oded Schramm and the ensuing revitalization of 2D critical phenomena as a stochastic evolution of geometry has been the one of the most spectacular theoretical developments in recent years. This development was honored by a Fields Metal in 2006 awarded to Wendelin Werner for foundational work done on SLE with O. Schramm and Greg Lawler. SLE has a vast web of interconnections with many areas of theoretical physics, including 2D conformal field theory, 2D quantum gravity, random matrix theory, multifractal properties of stochastic media, stochastic growth phenomena and many others. Moreover, surprising connections with 2D fully developed turbulence and 2D spin glasses have just recently emerged. The aim of this School is to provide an overview of these important and far-reaching recent developments by the leading experts in this field. Topics include: • Stochastic Loewner Evolution • 2D Conformal Field Theory • 2D Quantum Gravity • Multifractal Properties of Stochastic Systems • Stochastic Growth Processes • Connections with 2D Turbulence and Spin Glasses