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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Parameterized complexity is a branch of computational complexity theory in computer science that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input. In parameterized complexity, the complexity of a problem is measured as a function in two or more parameters of the input. This way, parameterized complexity achieves to classify NP-hard problems on a finer scale than this is possible in the classical setting, where the complexity of a problem is only measured by the number of bits in the input. The first systematic work on parameterized complexity was done by Downey & Fellows (1999).