The primary goal of this book is unifying and making more widely accessible the vibrant stream of research - spanning more than two decades - on the theory of semi-feasible algorithms. In doing so it demonstrates the richness inherent in central notions of complexity: running time, nonuniform complexity, lowness, and NP-hardness. The book requires neither great mathematical maturity nor an extensive background in computational complexity theory or in computer science. Another aim of this book is to lay out a path along which the reader can quickly reach the frontiers of current research, and...