A common theme in mathematics is to understand algebraic objects using their actions on geometric spaces. Bass—Serre theory is one instance of this approach where one studies groups via their actions on trees. I will give an introduction to the simplest case of Bass—Serre theory and build a dictionary between gluing of spaces, amalgamation of groups, and actions on trees. This dictionary gives us a surprising amount of information about the structure of groups, especially about their torsion subgroups. I will demonstrate this by applying the theory to SL2(Z), SL2(Q_p), and SL2(F_p((t))).