What are the key theorems of combinatorial group theory?
By "key theorems", I mean those most commonly used in the literature.
For added context, I have copies of "Presentation of Groups," by D. L. Johnson and "Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations," by Magnus et al., and I've just started a Ph.D. in the area.
I suppose a good place to start would be
Theorem (Nielson-Shreier Theorem): Every subgroup of a free group is itself free.
Update: I've got a copy of Lyndon & Schupp's "Combinatorial Group Theory".