The theory of flat (or foliated) fiber bundles is a rich subject at the intersection of topology, dynamics, geometry and foliation theory. This course will give an introduction to the area through discussion of accessible, low-dimensional examples and foundational results, including characteristic classes of flat bundles, dynamics of group actions on manifolds, bounded cohomology and the Euler class. I'll also devote some time to explaining techniques in new work on rigidity of geometric examples of flat circle bundles.