A glance at the table of contents will reveal that this textbook treats topics in analysis at the "Advanced Calculus" level. The aim has been to provide a development of the subject which is honest, rigorous, up to date, and, at the same time, not too pedantic. The book provides a transition from elementary calculus to advanced courses in real and complex function theory, and it introduces the reader to some of the abstract thinking that pervades modem analysis. This edition differs from the first in many respects. Point set topology is developed in the setting of general metric spaces as well as in Euclidean n-space,and two new chapters have been added on Lebesgue integration. The material on line integrals, vector analysis, and surface integraIs has been deleted. The order of some chapters has been rearranged, many sections have been completely rewritten, and several new exercises have been added.