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This lecture will start with electromagnetism and Maxwell's equations, consider the possibility of electric-magnetic duality and thus the existence of magnetic monopoles. Once the monopoles exist, Dirac showed that their charge must be quantized with respect to the electric charge (e.g. of an electron): This is called Dirac quantization. The naive Dirac monopole is singular, so we will construct a regular finite-energy magnetic monopole due to 't Hooft and Polyakov. The limit of the equations in which the potential vanishes is particularly interesting and are the original BPS equations. Their relation to instantons will be pointed out. Further, the monopole equations can be transformed using a transform due to Nahm, giving rise to the Nahm equations. The second part of the lecture will give very brief introductions to generalizations of the magnetic monopole: their non-Abelian extension (very briefly), the change of base space and the possibility of also possessing electric charges, giving rise to a new object called a Dyon due to Julia and Zee. Finally we are interested in the limit of a large number of monopoles, which is the subject of the monopole bag conjectures of Bolognesi. The limit can be understood roughly and asymptotically, but is not yet established with mathematical rigour (with a few exceptions).