These lecture notes discusses the developments both in the theoretical understanding of the physics and mathematics of magnetic monopoles as well as the ways in which they can be detected experimentally. The subject has now become highly interdisciplinary and recent monopole meetings have attracted participants from low temperature physics at one extreme to cosmology at the other. Contents:IntroductionMathematical Structures Underlying Monopoles in Gauge Theories:Dirac MonopoleNon-Abelian MonopolesConfigurations with Spherical and Axial SymmetryDyonsCompletely Integrable Equations for MonopolesBäcklund Trans-formations (W Nahm)Monopoles and Their Quantum Fields:Peculiar Angular Momentum States of Monopoles and Charged ParticlesQFT of Point Monopoles and RenormalizationQuantum Fluctuations of a 't Hooft-Polyakov MonopolesFermions Coupled to a 't Hooft-Polyakov MonopoleTheory of Monopole Catalysis of Proton DecayMonopole-Proton Cross SectionsFermion (N Craigie)Monopoles in Cosmology:Big Bang CosmologyPhase Transitions in Gauge TheoriesCosmological MonopolesMonopole Production in GUT Phase TransitionInflationary ScenarioInflation with SU(5)Inflation with Higher Dimensional Theories (Q Shifi)Monopoles and Astrophysics:Galactic Magnetic Fields and the Parker BoundAstronomical Flux Limits on Monopoles which can Catalyse (N Craigie)Conclusion: Prospects in Higher Dimensions. The Experimental Detection of Magnetic Monopoles:Summary of the Properties of Magnetic MonopolesInteraction of Monopoles with MatterMonopole DetectorsSearches for “Classical” MonopolesSearches for GUT MonopolesMonopole Catalysis of Proton DecayOther Types of Searches (G Giacomelli)and other papers Readership: Physicists and mathematicians. Review: “Altogether, the book gives a reasonably complete description of the state of the art in monopole physics at present.” C Cronström Mathematical Review (USA)