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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a monopole is a connection over a principal bundle G with a section (the Higgs field) of the associated adjoint bundle. The connection and Higgs field should satisfy the Bogomolnyi equation and be of finite action. Principal bundles have important applications in topology and differential geometry. They have also found application in physics where they form part of the foundational framework of gauge theories. Principal bundles provide a unifying framework for the theory of fiber bundles in the sense that all fiber bundles with structure group G determine a unique principal G-bundle from which the original bundle can be reconstructed.