With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, "Complex Analysis" will be welcomed by students of mathematics, physics, engineering and other sciences. "The Princeton Lectures in Analysis" represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which "Complex Analysis" is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing "Fourier" series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

《复分析》(原书第3版)的诞生已是半个世纪之前的事情，但是，深贯其中的严谨的学术风范以及针对不同时代所做出的切实改进使得它愈久弥新，成为复分析领域历经考验的一本经典教材。《复分析》(原书第3版)作者在数学分析领域声名卓著，多次荣获国际大奖，这也是《复分析》(原书第3版)始终保持旺盛生命力的原因之一。《复分析》(原书第3版)从现代数学的观点介绍复分析的基本知识与常用工具，全书共分为8章，主要包括：复数、复函数、作为映射的解析函数、复积分、级数与乘积展开、共形映射，软件克雷问题、椭圆函数以及全局解析函数，此外，大部分章节后都有练习，便于学生掌握书中内容。