Abstract. In a seminal paper published 20 years ago, Culler and Vogtmann suggested a way to investigate automorphisms of free groups by finding analogues of powerful geometric techniques invented by Thurston to study mapping classes of surfaces. Namely, they introduced a contractible space, called Outer space now, on which the group $Out(F_n)$ of outer automorphisms of a finitely generated free group acts properly. Outer space can be thought of as a combinatorial counterpart of Teichm\"uller space.