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.

本书全面叙述了代数学的基础知识，包括群论、环论、域论及主理想整环、多元多项式理论等。对于教授和学习方法也作了精心的安排，同时提出了多种建议。本书对许多数学术语的语源给出了较为详细的介绍；注重代数学与现代计算机理论知识的结合；许多概念都有作者本人的独到见解。另外，每一小节后均配有一定数量、难易不等的习题，书后还附有解答与提示，便于教学和自学。 本书可供高等院校数学系师生及相关工程技术人员参考。

《傅立叶分析导论》分为3部分：第1部分介绍傅立叶级数的基本理论及其在等周不等式和等分布中的应用；第2部分研究傅立叶变换及其在经典偏微分方程及Radom变换中的应用；第3部分研究有限阿贝尔群上的傅立叶分析。书中各章均有练习题及思考题。