For researchers and graduate students in relevant areas of analysis, Agarwal (National U of Singapore), Maria Meehan (Dublin City U.), and Donal O'Regan (National U. of Ireland-Galway) explain the fixed point theory. Beginning with the best known result, Banach's contraction theorem, they develop most of the main results and techniques, establish results for several classes of maps, and present the three main approaches to establishing continuation principles. Exercises are provided for courses or self-study.