Book excerpt: This book is devoted to metric fixed point theory. The goal is to develop, in a self-contained fashion, those results in this theory which involve the use of measures of noncompactness. Some of the well-known fixed point theorems are included with several applications to the theory of differential equations. This book is mainly addressed to graduate students who wish to learn about metric fixed point theory, but it will also be useful to researchers in the area. Most of the results presented here were obtained by the authors over the last ten years and have not previously appeared in any other textbook.