Significant progress has been made in the study of gauge theories in the last decade. Thanks to the discovery of novel techniques and especially supersymmetric localization, the field now possesses a plethora of exact results that previously seemed unreachable. Starting with the work of Nekrasov who computed the instanton partition function for N=2 theories in four dimensions, Pestun computed the exact partition function on a four-sphere for theories with N=2 supersymmetry. Shortly after the partition functions as well as other observables in various spacetime dimensions and compact manifolds were computed. Our school aims in deepening the understanding of current results and at investigating which of our current methods are transferable to theories with less supersymmetry, as well as trying to increase the list of possible observables that are computable via localization. Each week will feature three or four speakers giving one lecture per day. During the first week, in addition to these three one hour and a half lectures there will be discussion and homework sessions in the afternoon. During the second week, some of the lectures will be replaced by talks on more advanced topics.