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This book introduces the reader to fitted numerical methods for solving singularly perturbed differential equations. The performance of fitted methods is not adversely affected by the value of the perturbation parameter. The book concentrates on fitted mesh methods. These methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these methods work is far from simple. This book introduces the reader to the theory behind these novel numerical methods.