Recent advances in our understanding of the topology of 3-dimensional manifolds have led to a conjectural picture which indicates surprising restrictions on their topology. We will explore the major elements of this picture and what it says about basic classification and decision problems. The main themes to be addressed are the study of finite covers and virtual properties of 3-manifolds, the study of the set of all 3-manifolds and how they relate to each other, and the algebraic and geometric properties of 3-manifold fundamental groups and their character varieties. This event will consist of introductory mini-courses held during the first week, a workshop held during the second, and a series of Aisenstadt Chair lectures to be delivered by David Gabai (Princeton) which will provide a bridge between them.