Bass-Serre theory is a theory that deals with group actions on trees and analyzes the algebraic structure of groups. It is a powerful tool but also there are many examples of groups that do not have any group actions that the theory applies to.

We study group actions on a "quasi-tree", which is a geodesic space that looks like a tree. It turns out that this generalization is useful. I will discuss constructions of quasi-trees with group actions. This is a joint work with Bestvina and Bromberg.