This text starts on an intermediate level of generality: sufficiently general to convey to the student the flavor of abstract methods in analysis and to cover many important applications, and still down-to-earth to make easy reading for beginners. The tradition founded by Banach, and favorable experiences from many courses, point to metric spaces as a suitable initial subject, and the present book keeps in this tradition ... The authors have selected and presented in a clear and readable way the basic material which is most likely to be used frequently. A wealth of examples, counterexamples, applications and exercises accompany the abstract theory throughout.

An attractive feature of the book is that each major theorem is followed by ... illustrations of its use. There are many well-chosen problems. Some problems ask the reader to apply an abstract idea to a concrete situation and others ask the reader to develop more theory.