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.

Since its birth in Poincaré's seminal 1894 "Analysis Situs", topology has become a cornerstone of mathematics. As with all beautiful mathematical concepts, topology inevitably — resonating with that Wignerian principle of the effectiveness of mathematics in the natural sciences — finds its prominent role in physics. From Chern–Simons theory to topological quantum field theory, from knot invariants to Calabi–Yau compactification in string theory, from spacetime topology in cosmology to the recent Nobel Prize winning work on topological insulators, the interactions between topology and physics have been a triumph over the past few decades.
In this eponymous volume, we are honoured to have contributions from an assembly of grand masters of the field, guiding us with their world-renowned expertise on the subject of the interplay between "Topology" and "Physics". Beginning with a preface by Chen Ning Yang on his recollections of the early days, we proceed to a novel view of nuclei from the perspective of complex geometry by Sir Michael Atiyah and Nick Manton, followed by an entrée toward recent developments in two-dimensional gravity and intersection theory on the moduli space of Riemann surfaces by Robbert Dijkgraaf and Edward Witten; a study of Majorana fermions and relations to the Braid group by Louis H Kauffman; a pioneering investigation on arithmetic gauge theory by Minhyong Kim; an anecdote-enriched review of singularity theorems in black-hole physics by Sir Roger Penrose; an adventure beyond anyons by Zhenghan Wang; an aperçu on topological insulators from first-principle calculations by Haijun Zhang and Shou-Cheng Zhang; finishing with synopsis on quantum information theory as one of the four revolutions in physics and the second quantum revolution by Xiao-Gang Wen. We hope that this book will serve to inspire the research community.

These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.

《拓扑学导论》基于作者在莫斯科独立大学开设代数拓扑与微分拓扑导论课程的讲义编写。作者介绍了拓扑学的经典概念与方法，这些内容对本领域的专家是不可或缺的，对于数学研究者与理论物理专家也十分有用。特别地，作者介绍了与流形、胞腔空间、覆叠与纤维映射、同伦群、同调与上同调、相交指标等内容相关的一些思想和结果。
《拓扑学导论》可供数学及理论物理专业的教师和大学生使用。

《纤维丛(第3版)》讲述了：The notion of a fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950, the definition of fibre bundle had been clearly formulated, the homotopy classification of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians: Chern, Pontrjagin, Stiefel, and Whitney. Steenrod's book, which appeared in 1950, gavea coherent treatment of the subject up to that time.
About 1955, Miinor gave a construction ora universal fibre bundle for any topological group. This construction is also included in Part I along with an elementary proof that the bundle is universal.

《21世纪数学规划教材·数学基础课系列:点集拓扑与代数拓扑引论》是高等院校数学系本科生拓扑学的入门教材。全书共分五章。第一章介绍拓扑空间和连续映射等基本概念。第二章介绍可数性、分离性、连通性、紧致性等常用点集拓扑性质。第三章从几何拓扑直观和代数拓扑不变量两个角度，综合地介绍了闭曲面的分类。第四章介绍了基本群的概念以及应用。第五章介绍复迭空间的技术。《21世纪数学规划教材·数学基础课系列:点集拓扑与代数拓扑引论》的特点是叙述浅显易懂，并给出了丰富具体的例子，主干内容（不打星号的节）每节均配有适量习题，书末附有习题的提示或解答。

《纽结理论中的亚历山大多项式与琼斯多项式:从1道北京市高1数学竞赛试题谈起》从一道北京市高中一年级数学竞赛试题谈起，介绍了纽结理论、亚历山大多项式、琼斯多项式的基本知识、起源和发展等问题。全书共八章，读者可以较全面地了解这一类问题的实质，并且还可以认识到它在许多学科中的应用。

本书由菲尔兹奖和沃尔夫奖得主 J.W. Milnor 所著，是一本蜚声国际数学界的经典之作。内容涉及光滑流形和光滑映射，Sard 定理和 Brown 定理，映射的模2度，定向流形，向量场与 Euler 数，标架式协边，Pontryagin 构造等。全书内容简要，短小精悍。
本书为双语版，可用于双语教学。既适合高等院校数学专业高年级本科生和研究生阅读，也可供对微分拓扑有兴趣的专业人士参考。