Mathematicians have been studying notions of space and geometry for thousands of years. Over time our models for spaces have grown successively more abstract. A major conceptual leap in the 1960's was taken with the theory of algebraic stacks, which are a sort of space with "internal symmetries'' not visible in usual geometric objects. There has been a flurry of recent activity among mathematical researchers in understanding the structure of these spaces. This workshop will bring together researchers developing this state-of-the-art theory with mathematicians at various career stages who are interested in applying this theory in their work. The organizers hope that this week of focused discussion on this topic will help bring these methods to a wider audience and lead to significant new developments both in the foundations of the theory and in applications.