In this talk, I would like to give a recent progress of my study on Extremal length geometry on Teichmueller space. This research is aimed for unifying (or understanding the relation between) the complex analytical aspect and the topological aspect of Teichmueller theory in the framework of the Thurston theory. Extremal length geometry is expected to act as a mediator at the unification. If time permits, I will explain my program for the unification.

(Time and venue has changed!)