  A summary introduction of the Weil-Petersson metric space geometry is
presented. Teichmueller space and its augmentation are described in terms of
Fenchel-Nielsen coordinates. Formulas for the gradients and Hessians of
geodesic-length functions are presented. Applications are considered. A
description of the Weil-Petersson metric in Fenchel-Nielsen coordinates is
presented. The Alexandrov tangent cone at points of the augmentation is
described. A comparison dictionary is presented between the geometry of the
space of flat tori and Teichmueller space with the Weil-Petersson metric.
