《代数基本概念》是沙法列维奇的经典名著之一，目的是对代数学、它的基本概念和主要分支提供一个一般性的全面概述，论述代数学及其在现代数学和其他科学中的地位。
《代数基本概念》高度原创且内容充实，涵盖了代数中所有重要的基本概念，不只是域、群、环、模，而且包括群表示、lie群与lie代数、上同调、范畴论等。它不是按照代数教科书的传统模式写的，而是反映了作者的强烈观点：“用基本例子的一批样本，它会表达得更好。这给数学家提供了动机和实质性的定义，同时给出这个概念的真实意义。”
书中共有精心挑选的164个例子和45幅图，给读者提供了物理背景和直觉，通过它们能够对抽象的概念产生更深的印象。相对而言，书中只有6个引理和104个定理，而且这些定理往往不加证明，只给出证明思路，这将大大刺激读者的思考，激发更大的兴趣。
《代数基本概念》起点并不高，大学数学系二、三年级的学生能够读懂大部分内容。本书文前附季理真撰写的有关本书作者和本书内容的精彩介绍。读者对象是大学数学系的学生、数学专业任何方向的研究生、教师和研究工作者，包括已经成名的数学家。理论物理学家和其他自然科学领域的专家也会对本书有兴趣。

This book provides an introduction to abstract algebraic geometry using the methods of schemes and cohomology. The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a number of basic concepts and examples. Then the methods of schemes and cohomology are developed in Chapters II and III, with emphasis on applications rather than excessive generality. The last two chapters of the book (IV and V) use these methods to study topics in the classical theory of algebraic curves and surfaces.
本书为英文版。

《初等几何的著名问题》是著名数学家F.Klein 1894年在德国哥廷根的一个讲稿，主要讨论了初等几何的三大著名难题——倍立方、三等分角，圆的求积。当年作者用简明易懂的方式讲解这个课题，引起听众极好的反响。后由德国数学家帮助整理出版，1930年又翻译成英文，一直流传至今。.

代数拓扑的微分形式，ISBN：9787506201124，作者：（美）Raoul Bott，（美）Loring W.Tu著

Algebraic topology is a basic part of modern mathematics and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry and Lie groups. This book provides a treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology and the book concludes with a list of suggested readings for those interested in delving further into the field.

《代数几何原理》主要内容：A third general principle was that this volume should be stir-contained.In particular any "hard" result that would be utilized should be fullyproved. A difficulty a student often faces in a subject as diverse as algebraic geometry is the profusion of cross-references, and this is one reason for attempting to be self-contained. Similarly, we have attempted to avoid allusions to, or statements without proofs of, related results. This book is in no way meant to be a survey of algebraic geometry, but rather is designed to develop a working facility with specific geometric questions.Our approach to the subject is initially analytic: Chapters 0 and 1 treat the basic techniques and results of complex manifold theory, with some emphasis on results applicable to projective varieties. Beginning in Chapter 2 with the theory of Riemann surfaces and algebraic curves, and continu-ing in Chapters 4 and 6 on algebraic surfaces and the quadric line complex, our treatment becomes increasingly geometric along classicallines. Chapters 3 and 5 continue the analytic approach, progressing to more special topics in complex manifolds.

《交换代数(英文影印版)》主要内容：It has seemed to me for a long time that commutative algebra is best practiced with knowledge of the geometric ideas that played a great role in its formation: in short, with a view toward algebraic geometry.Most texts on commutative algebra adhere to the tradition that says a subject should be purified until it references nothing outside itself. There are good reasons for cultivating this style; it leads to generality, elegance, and brevity, three cardinal virtues. But it seems' to me unnecessary and undesirable to banish, on these grounds, the motivating and fructifying ideas on which the discipline is based.

本书是根据美国科学院院士，著名数学家P·格列菲斯在北京大学讲课的讲稿整理写成的。本书篇幅虽不大，但内容丰富，阐述精炼，引人入胜。书中深入浅出地介绍了正则化定理，Riemann-Roch定理，Abel定理等代数曲线论的重要结果，以及这些定理的应用和重要的几何事实。读者只要具有大学复变函数论和抽象代数的基础知识即可阅读此书。 本书可作为大学数学系高年级学生和研究生教材，也可供数学工作者参考。

This extraordinary volume contains a large part of the mathematical correspondence between A. Grothendieck and J.-P. Serre. It forms a vivid introduction to the study of algebraic geometry during the years 1955-1965. During this period, algebraic geometry went through a remarkable transformation, and Grothendieck and Serre were among central figures in this process. In the book, the reader can follow the creation of some of the most important notions of modern mathematics, such assheaf cohomology, schemes, Riemann-Roch type theorems, algebraic fundamental group, motives, etc. The letters also reflect the mathematical and political atmosphere of this period (Bourbaki, Paris, Harvard, Princeton, war in Algeria, etc.). Also included are letters written between 1984 and 1987. Theletters are supplemented by J-P.Serre's notes, which give explanations, corrections, and references to further results. The book is a unique bilingual (French and English) volume. The original French text is supplemented here by the English translation, with French text printed on the left-hand pages and the corresponding English text printed on the right. The book also includes several facsimiles of original letters. The original French volume was edited by Pierre Colmez and J-P. Serre. TheEnglish translation for this volume was translated by Catriona Maclean and edited by J-P. Serre and Leila Schneps. The book should be useful to specialists in algebraic geometry, mathematical historians, and to all mathematicians who want to experience the unfolding of great mathematics.

Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas.
This text consists of a series of exercises, plus some background information and explanations, starting with conics and ending with sheaves and cohomology. The first chapter on conics is appropriate for first-year college students (and many high school students). Chapter 2 leads the reader to an understanding of the basics of cubic curves, while Chapter 3 introduces higher degree curves. Both chapters are appropriate for people who have taken multivariable calculus and linear algebra. Chapters 4 and 5 introduce geometric objects of higher dimension than curves. Abstract algebra now plays a critical role, making a first course in abstract algebra necessary from this point on. The last chapter is on sheaves and cohomology, providing a hint of current work in algebraic geometry.

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: 1. the log likelihood function can be given a common standard form using resolution of singularities, even applied to more complex models; 2. the asymptotic behaviour of the marginal likelihood or 'the evidence' is derived based on zeta function theory; 3. new methods are derived to estimate the generalization errors in Bayes and Gibbs estimations from training errors; 4. the generalization errors of maximum likelihood and a posteriori methods are clarified by empirical process theory on algebraic varieties.

This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. It includes features such as: first full treatment of the subject and its applications; written by the pioneer of this field; broad applications in mathematics; of interest across most fields; ideal as an introduction and survey; examples treated include: @subbul; the space of Penrose tilings; the space of leaves of a foliation; the space of irreducible unitary representations of a discrete group; the phase space in quantum mechanics; the Brillouin zone in the quantum Hall effect; and a model of space time.

One of the major discoveries of the last two decades of the twentieth century in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the a comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.