Introduction
Energy Estimates for S1-Valued Maps
A Lower Bound for the Energy of S1-Valued Maps on Perforated Domains
Some Basic Estimates for uɛ
Toward Locating the Singularities: Bad Discs and Good Discs
An Upper Bound for the Energy of uɛ away from the Singularities
uɛ_n: u-star is Born! - u-star Coincides with THE Canonical Harmonic Map having Singularities (aj)
The Configuration (aj) Minimizes the Renormalization Energy W
Some Additional Properties of uɛ
Non-Minimizing Solutions of the Ginzburg-Landau Equation
Open Problems.