This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering students. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject. Salient Features: 1. Written in easy simple language, integration is described with a high degree of abstraction across the text. 2. Entirely new chapter on differentiation in this edition 3. Parts of certain chapters have been simplified and explained in more detail.