《黎曼几何》主要内容：The object of this book is to familiarize the reader with the basic language of and some fundamental theorems in Riemannian Geometry. To avoid referring to previous knowledge of differentiable manifolds, we include Chapter 0, which contains those concepts and results on differentiable manifolds which are used in an essential way in the rest of the book。
The first four chapters of the book present the basic concepts of Riemannian Geometry (Riemannian metrics, Riemannian connections, geodesics and curvature). A good part of the study of Riemannian Geometry consists of understanding the relationship between geodesics and curvature. Jacobi fields, an essential tool for this understanding, are introduced in Chapter 5. In Chapter 6 we introduce the second fundamental form associated with an isometric immersion, and prove a generalization of the Theorem Egregium of Gauss. This allows us to relate the notion of curvature in Riemannian manifolds to the classical concept of Gaussian curvature for surfaces。

《黎曼几何引论(上)》可供综合大学、师范院校数学系、物理系学生和研究生作用教材，并且可供数学工作者参与。“黎曼几何引论”课是基础数学专业研究生的基础课。从1954年黎曼首次提出黎曼几何的概念以来，黎曼几何学经历了从局部理论到大范围理论的发展过程。现在，黎曼几何学已经成为广泛地用于数学、物理的各个分支学科的基本理论。《黎曼几何引论(上)》上册是“黎曼几何引论”课的教材，前四章是黎曼几何的基础；第五与第六章介绍黎曼几何的变分方法，是大范围黎曼几何学的初步；第七章介绍黎曼几何子流形的理论。每章末都附有大量的习题，书末并附有习题答案和提示，便于读者深入学习和自学。

本书是作者多年来在北京大学为硕士研究生开设抽象代数课程的讲义，书中系统讲述了抽象代数的基本理论和方法。它反映了新时期硕士研究生抽象代数课程的教学理念，凝聚了作者及同事们所积累的丰富教学经验。全书共分为六章，内容包括：预备知识，模，群的进一步知识，Galois 理论，结合代数和有限群的表示论，典型群的初步知识等。每章配备适量习题，书末附有习题的解答或提示，供读者参考。.
本书作为研究生教材，既注意内容的基础性又兼顾先进性。考虑到硕士生来自不同学校，而在本科阶段所学的抽象代数内容不尽相同，为了使读者有一个共同的基础，本书在前三章都加了第0节，分别介绍在本科低年级抽象代数I中已学过的环论、群论和域论知识。本书在叙述上由浅入深、循序渐进、语言精练、清晰易懂，并注意各章节之间的内在联系与呼应，便于教学与自学。..
本书可作为综合大学、高等师范院校数学系高年级本科生、研究生的教材或教学参考书，也可供数学工作者阅读。...

本书是综合大学、高等师范院数学系研究生基础课教材，全书共分五章，系统讲述同调论的基本理论和方法。
本书的主线是奇异同调的理论框架和胞腔同调的计算方法，单纯同调作为胞腔同调的特殊情形来处理。前三章讲加法结构，基本上采取传统的讲法。第四章讲乘法结构，综合了奇异同调和胞腔同调这两个不同的角度。第五章流形的论述比较新颖，在胞腔流形上建立起互相对称的对偶剖分，给对偶定理提供了清晰的几何图景。这虽是古朴的思路，却是文献中所未见的。
本书在选材上注重概念、方法、结论、应用，充分反映同调论的核心内容；在内容处理上强调几何背景，举例丰富，图文并茂；在叙述上语言精炼而清晰易懂，注意各章节之间的联系呼应，便于教学与自学。每节配有适量的习题和思考题，以帮助读者理解和掌握。
本书可作为综合大学、高等师范院校数学研究生、高年级大学生的教材或教学参考书，也可供数学工作者阅读。

This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard's theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.

《有限群的线性表示》是一部非常经典的介绍有限群线性表示的教程，原版曾多次修订重印，作者是当今法国最突出的数学家之一，他对理论数学有全面的了解，尤以著述清晰、明了闻名。《有限群的线性表示》是他写的为数不多的教科书之一，原文是法文(1971年版)，后出了德译本和英译本。《有限群的线性表示》是英译本的重印本。它篇幅不大，但深入浅出的介绍了有限群的线性表示，并给出了在量子化学等方面的应用，便于广大数学、物理、化学工作者初学时阅读和参考。

Written for readers with modest mathematical backgrounds, this book contains numerous exercises and examples at varied levels and provides a well-motivated introduction to the classical formulation of class field theory--placing great importance on the explicit numerical example to illustrate the power of basic theorems in various situations. It includes an elementary treatment of quadratic forms and genus theory; addresses when a prime p is of the form x2+ny2; features new coverage of Shimura reciprocity law; and includes simultaneous treatment on elementary and advanced aspects of number theory.

雅克·拉康是最富挑战性与争议性的当代思想家之一，也是自弗洛伊德以来最具影响力的精神分析学家。拉康理论的影响远远超出了诊疗室的范围，从而波及到了诸如文学理论、电影理论、性别理论与社会理论等不同的学科。本书不但完整地涵盖了拉康的学术生涯，而且还针对一些拉康的概念以及他关于这些概念的作品而为读者提供了一部通俗易懂的导读，这些概念包括：
• 想象界（Imaginary）与象征界（Symbolic）
• 俄狄浦斯情结（Oedipus complex）与阳具的意义（meaning of the phallus）
• 主体（subject）与无意识（unconscious）
• 实在界（Real）
• 性别差异（sexual difference）
肖恩·霍默（Sean Homer）把拉康的作品定位在了当代法国思想与精神分析历史的语境之中，因而他的这本《导读拉康》是对于这位极具影响的理论家的一部理想的导读。

"Real Analysis" is the third volume in the "Princeton Lectures in Analysis", a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis. The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises. As with the other volumes in the series, "Real Analysis" is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels.

This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen-Macaulay rings, have been added. This book is ideal as a route into commutative algebra.

《泛函分析学习指南》是高等院校高年级本科生泛函分析课程的辅导教材，可与国内通用的泛函分析教材同步使用，特别适合于作为《泛函分析讲义（上册）》（张恭庆、林源渠编著，北京大学出版社）的配套辅导教材。共分四章，内容包括度量空间、线性算子与线性泛函、广义函数与索伯列夫空间、紧算子与Fredholm算子。每小节按基本内容、典型例题精解两部分编写。基本内容简明介绍了读者应掌握的基础知识；典型例题精解按照基础题、规范题、综合题三种类型，从易到难，循序渐进，详细讲述例题的解法，并对解题方法进行归纳和总结，以帮助学生克服由于不适应泛函分析中全新的研究对象和处理问题的方法所产生的困惑，同时也为任课教师提供一些便利条件。

这是一部泛函分析教材。它系统地介绍线性泛函分析的基础知识。全书共分四章： 度量空间；线性算子与线性泛函；广义函数与Coболев空间；以及紧算子与Fredholm算子。《泛函分析讲义(上)》的主要特点是它侧重于分析若干基本概念和重要理论的来源和背景，强调培养读者运用泛函方法解决问题的能力，注意介绍泛函分析理论与数学其它分支的联系。书中包含丰富的例子与应用，对于掌握基础理论有很大帮助。此书适用于理工科大学本科生与研究生阅读，并且可供一般的数学工作者、物理工作者、工程技术人员参考。为便于读者学习，本次重印书末增加了习题补充提示和索引，以供读者参考。

Product Description
Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. With the minimum of prerequisites, Dr. Reid introduces the reader to the basic concepts of algebraic geometry, including: plane conics, cubics and the group law, affine and projective varieties, and nonsingularity and dimension. He stresses the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book contains numerous examples and exercises illustrating the theory.

In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book.

Commutative ring theory is important as a foundation for algebraic and complex analytical geometry and this text covers the basic material with a solid knowledge of modern algebra as the only prerequisite.