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 meet and engage the many exciting open problems in this area.

This book presents a consolidated survey of the vibrant field of research known as the theory of semi-feasible algorithms. This research stream perfectly showcases the richness of, and contrasts between, the central notions of complexity: running time, nonuniform complexity, lowness, and NP-hardness. Research into semi-feasible computation has already developed a rich set of tools, yet is young enough to have an abundance of fresh, open issues. Being essentially self-contained, the book requires neither great mathematical maturity nor an extensive background in computational complexity theory or in computer science in general. Newcomers are introduced to the field systematically and guided to the frontiers of current research. Researchers already active in the field will appreciate the book as a valuable source of reference.