The moduli space of Euclidean tori is the modular orbifold (cont'd)

After recapping the correspondence between the upper half-plane and the collection of marked Euclidean structures on the two-dimensional torus, I will describe the correspondence between the natural SL(2,Z)-actions on these spaces.  Then I will use the Farey tessellation, an SL(2,Z)-invariant triangulation of the upper half-plane, to give a concrete description of the modular orbifold.  Finally, I will pull this back to a description of the moduli space of the title.