I am a PhD freshman working on topological graph theory and geometric group theory. I would like to learn some Bass-Serre theory. What do you think is the best introductory textbook in this topic? Thank you in advance for your recommendations.



Bass-Serre theory textbook
As mentioned by Andy Putman in the comments, the classical (and probably the best) references are Serre's book *Trees* and Scott and Wall's paper *Topological methods in group theory*.


Serre's approach is elementary and essentially self-contained, based on combinatorial arguments. Scott and Wall's approach is based on algebraic topology (in particular, they use covering theory). If you are already familiar with some algebraic topology, then you may find Scott and Wall's approach more intuitive, more visual. Personally, I began by reading Serre's book, but I prefer the point of view of graphs of spaces.


You can also take a look at Henry Wilton's blog [Geometric group theory](https://392c.wordpress.com/). There are several blogposts dedicated to the Bass-Serre theory. In complement to Serre's book, an interesting complement is Higgins' article *The fundamental groupoid of a graph of groups*. Looking at the fundamental groupoid instead of the fundamental group makes some arguments more natural.


