This monograph addresses the field theoretical aspects of magnetic monopoles. Written for graduate students as well as researchers, the author demonstrates the interplay between mathematics and physics. He delves into details as necessary and develops many techniques that find applications in modern theoretical physics. This introduction to the basic ideas used for the description and construction of monopoles is also the first coherent presentation of the concept of magnetic monopoles. It arises in many different contexts in modern theoretical physics, from classical mechanics and electrodynamics to multidimensional branes. The book summarizes the present status of the theory and gives an extensive but carefully selected bibliography on the subject. The first part deals with the Dirac monopole, followed in part two by the monopole in non-abelian gauge theories. The third part is devoted to monopoles in supersymmetric Yang-Mills theories.

Résumé
One would be surprised if Nature had made no use of it. P.A.M. Dirac According to some dictionaries, one meaning of the notion of beauty is symmetry. Probably, beauty is not entirely in the eye of the beholder. It seemstoberelatedtothesymmetryoftheobject.Fromaphysicalviewpoint, this de?nition is very attractive: it allows us to describe a central concept of theoretical physics over the last two centuries as being a quest for higher symmetry of Nature. The more symmetric the theory, the more beautiful it looks. Unfortunately, our imperfect (at least at low-energy scale) world is full of nasty broken symmetries. This has impelled physicists to try to understand how this happens. In some cases, it is possible to reveal the mechanism of violationandhowthesymmetrymayberecovered;thenourpictureofNature becomes a bit more beautiful. One of the problems of the broken symmetry that we see is that, while there are electric charges in our world, their counterparts, magnetic mo- poles, have not been found. Thus, in the absence of the monopoles, the s- metry between electric and magnetic quantities is lost. Can this symmetry be regained? In the history of theoretical physics, the hypothesis about the possible existence of a magnetic monopole has no analogy. There is no other purely theoretical construction that has managed not only to survive, without any experimental evidence, in the course of more than a century, but has also remained the focus of intensive research by generations of physicists.

Contenu
Dirac Monopole.- Magnetic Monopole in Classical Theory.- The Electron-Monopole System:Quantum-Mechanical Interaction.- Topological Roots of the Abelian Monopole.- Abelian Monopole: Relativistic Quantum Theory.- Monopole in Non-Abelian Gauge Theories.- 't Hooft-Polyakov Monopole.- Multimonopole Configurations.- SU(2) Monopole in Quantum Theory.- Monopoles Beyond SU(2) Group.- Monopoles and the Problem of Confinement.- Fermions in the Field of Non-Abelian Monopole and RubakovCallan Effect.- Supersymmetric Monopoles.- Construction of Supersymmetric Yang-Mills Theories.- Magnetic Monopoles in the N = 2 Supersymmetric Yang-Mills Theory.- SeibergWitten Solution of N = 2 SUSY YangMills Theory.