Complexity is a puzzling and important concept in contemporary research in many disciplines. This book addresses the problem of defining complexity by carefully analysing in what sense complexity means measure in such areas as the theory of dynamical systems, condensed matter physics, ecology, immunology and the theory of neural networks. The information content of complexity is studied and similarities and differences in the various concepts of complexity are highlighted, sometimes provocatively. The book could open the way to finding a paradigm of complexity, and should become a standard reference for a wide audience of researchers in the physical and biological sciences.