Preface.- Selfdual Gauge Field Theories.- Elliptic Problems in the Study of Self-ual Vortex Configurations.- Planar Self-dual Chern-Simons Vortices.- Periodic Selfdual Chern-Simons Vortices.- The Analysis of Liouville-type Equations with Singular Sources.- Mean Field Equations of Liouville-type.- Selfdual Electroweak Vortices and Strings.- References.- Index.

This monograph discusses specific examples of selfdual gauge field structures, including the Chern-Simons model, the abelian-Higgs model, and Yang-Mills gauge field theory. The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of gauge theory and formulating examples of Chern-Simons-Higgs theories (in both abelian and non-abelian settings). Thereafter, the Electroweak theory and self-gravitating Electroweak strings are examined. The final chapters treat elliptic problems involving Chern-Simmons models, concentration-compactness principles, and Maxwell-Chern-Simons vortices.