In 1994, Seiberg and Witten introduced new sets of invariants for four-manifolds, which were considerably more tractable than Donaldson's and led to new advances in geometry and topology in dimension 4. Methods have been developed to understand the nature of these invariants in greater depth, and this book is a step in that direction, where we discuss how to glue monopoles in a quite general setting, and the conditions under which this is possible. This will result in a local fiber-product description for the moduli space when the 4-manifold under consideration is split into two pieces along a separating 3-dimensional sub-manifold, and will give us a great deal of insight into the structure of Seiberg-Witten moduli spaces. The book should be accessible to graduate students and mathematicians working in this field.

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