This book has developed over a number of years. The aim has been to give a unified and coherent account of the many and various parts of general recursion theory. I have not worked alone. The Recursion Theory Seminar in Oslo has for a number of years been a meeting place for an active group of younger people. Their work and enthusiasm have been an important part of the present project. I am happy to acknowledge my debts to Johan Moldestad, Dag Normann, Viggo Stoltenberg-Hansen and John Tucker. It has been a great joy for me to work together with them.