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"*.