We will study a generalized version of what is known as Fraïssé's method in model theory to elementary embeddings. The method allows us to obtain for certain classes of structures a limit structure which is universal (i.e. all members of the class embed elementarily in the limit), saturated and homogeneous. A quick discussion of theorems solving Tarski's problem together with the preparations in the previous talk will then allow us to prove that groups elementarily equivalent to a fixed torsion-free hyperbolic group form such a strong elementary Fraïssé class, and consequently prove the existence of a universal, saturated and homogenous elementary free group.