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.

《费马大定理》是关于一个困惑了世间智者358年的谜题的传奇。本书既有振奋人心的故事讲述方式，也有引人入胜的科学发现的历史。西蒙•辛格讲述了一个英国人，经过数年秘密辛苦的工作，终于解决了最具挑战性的数学问题的艰辛旅程。

由A.C.米先柯和A.T.福明柯编著的《微分几何与拓扑学简明教程》是俄
罗斯数学教材选译系列之一，是微分几何教程的简明阐述，在大学数学系两
个学期中讲授。内容包含：一般拓扑，非线性坐标系，光滑流形的理论，曲
线论和曲面论，变换群，张量分析和黎曼几何，积分法和同调论，曲面的基
本群，黎曼几何中的变分原理。叙述中用大量的例子说明并附有习题，常有
补充的材料。
《微分几何与拓扑学简明教程》适合数学、物理及相关专业的高年级本
科生、研究生、高校教师和研究人员参考使用。

本书作者在拓扑学领域享有盛誉。
本书分为两个独立的部分；第一部分普通拓扑学，讲述点集拓扑学的内容；前4章作为拓扑学的引论，介绍作为核心题材的集合论、拓扑空间。连通性、紧性以及可数性和分离性公理；后4章是补充题材；第二部分代数拓扑学，讲述与拓扑学核心题材相关的主题，其中包括基本群和覆盖空间及其应用。
本书最大的特点在于对理论的清晰阐述和严谨证明，力求让读者能够充分理解。对于疑难的推理证明，将其分解为简化的步骤，不给读者留下疑惑。此外，书中还提供了大量练习，可以巩固加深学习的效果。严格的论证，清晰的条理、丰富的实例，让深奥的拓扑学变得轻松易学。

本书是作者上世纪60年代出版的《分析教程》的第二卷，曾被译为英文和西班牙文，内容包括拓扑和函数空间。本书针对有一定数学基础的大学生，但几乎不要求任何预备知识。使其能在一个尽可能简单的框架上了解现代分析的有力工具及其应用。
书中的基本概念几乎都在其一般形式下来介绍，并通过例子来说明所选择定义的合理性。例如，在叙述任意拓扑空间时，先简要讨论实数直线；而距离空间则在提出一致性问题后才引入；同样，赋范向量空间和Hilbert空间仅在讨论局部凸空间后引入，后者在现代分析及其应用中越来越重要。书中通过大量的例子及反例来说明定理成立的确切范围，并设置了各种难度的习题，便于学生检验其对课程的理解程度并锻炼自身的创新能力。
本书可供高等院校数学及相关专业的本科生、研究生以及教师参考。

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