"This book deals with the mathematical study of the two-dimensional Ginzburg-Landau model with magnetic field. This important model was introduced by Ginzburg and Landau in the 1950s as a phenomenological model to describe superconductivity consisting in the complete loss of resistivity of certain metals and alloys at very low temperatures...All parts of this interesting book are clearly and rigorously written. ... Read moreA consistent bibliography is given and several open problems are detailed. This work has to be recommended." —Zentralblatt MATH "In conclusion, this book is an excellent, up-to-the-minute presentation of the current state of the mathematics of vortices in Ginzburg-Landau models. It also represents a tour de force of mathematical analysis, revealing a fascinating and intricate picture of a physical model which may have been unexpected based on heuristic considerations. I strongly recommend this book to researchers who are interested in vortices (andother quantized singularities) as these methods will continue to be instrumental in forthcoming research in the field. One could also find interesting material to supplement a graduate coursc in variational methods or PDEs." —SIAM Review Show Less