Credlts for Figures and Color Plates Much has changed in the world of fractals, computer graphics and modem mathematics since the first edition of Fractals Everywhere appeared. The company Iterated Systems, Inc., founded by Michael Barnsley and Alan Sloan, is now competing in the image compression field with both hardware and software products that use fractal geometry to compress images. Indeed, there is now a plethora of texts on subjects like fractals and chaos, and these terms are rapidly becoming "household words.

The preface to a textbook frequently contains the author's justification for offering the public "another book" on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia.Considering the vast amount of research currently being done in this area,the paucity of introductory texts is somewhat surprising. Parts of the theory are contained in various books of Lang (especially [La 3] and [La 5]); and there are books of Koblitz ([Ko]) and Robert ([Rob], now out of print) which concentrate mostly on the analytic and modular theory. In addition, survey articles have been written by Cassels ([Ca 7], really a short book) and Tate ([Ta 5]. which is beautifully written, but includes no proofs). Thus the author hopes that this volume will fill a real need, both for the serious student who wishes to learn the basic facts about the arithmetic of elliptic curves; and for the research mathematician who needs a reference source for those same basic facts.

Riemannian geometry is characterized, and research is oriented towards and shaped by concepts (geodesics, connections, curvature, ...) and objectives, in particular to understand certain classes of (pact) Riemannian manifolds defined by curvature conditions (constant or positive or curvature, ...). By way of contrast, geometric analysis is a perhaps somewhat less systematic collection of techniques, for solving extremal problems naturally arising in geometry and for investigating and characterizing their solutions. It turns out that the two fields plement each other very well; geometric analysis offers tools for solving difficult problems in geometry, and Riemannian geometry stimulates progress in geometric analysiy setting ambitious goals. It is the aim of thiook to be a systematic and prehensive introduction to Riemannian geometry and a representative introduction to the methods of geometric analysis. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds.

法雷尔编著的《流形拓扑导论讲义(精)》的内容涵盖了流形拓扑学最基本的思想与结果，包括h—与s—配边定理，Pontryagin类的拓扑不变性、手术理论、代数K理论等，可以作为初学者进入这一领域的“路标”。《流形拓扑导论讲义(精)》可作为几何与拓扑领域的研究生教材或参考书，也可以供相关研究人员参考。

This volume of the Encyclopaedia contains two articles which give a survey of modern research into non-regular Riemannian geometry，carried out mostly by Russian mathematicians． The first article written by Reshetnyak is devoted to the theory of two—dimensional Riemannian manifolds of bounded curvature．Concepts of Riemannian geometry such as the area and integral curvature of a set and the length and integral curvature of a curve are also defined for these manifolds．Some fundamental results of Riemannian geometry like the Gauss．Bon formula are true in the more general case considered in the book． The second article by Berestovskij and Nikolaev is devoted to the theory of metric spaces whose curvature lieetween two giyen constants．The main result iS that these spaces are in fact Riemannian． This result has important applications in global Riemannian geometry． Both parts cover topics which have not yet been treated in monograph form．Hence the book will be immensely useful to

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 plex 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 plex, our treatment bees increasingly geometric along classicallines. Chapters 3

这本书旨在让读者清晰明了地接触广义相对论，广义相对论的引入，从大爆炸到黑洞，这样很容易激起读者对物理学的浓厚兴趣。附录中提供了大量的数学材料来帮助读者理解正文，而且附录的很多部分本身也是独立完整的。 本书的结构，章主要介绍狭义相对论和基本张量代数，包含一个场论的简要概述。紧接着的两章引入流形和曲率，包含一些具有激发性的物理知识，但主要目标是建立数学框架。第四章引入广义相对论，并且给出一些择一性定理的讨论。紧接着的四章主要讨论广义相对论的主要用途：黑洞，扰动理论和引力波，以及宇宙学。这些章节都贯穿有试验性结论的讨论，使得这些理论的实用性马上显现出来。 本书很适合物理系高年级本科生、研究生以及对广义相对论感兴趣的读者。 注：本书为全英文版。

StephenS.Kudla是加拿大多伦多大学的研究教授，是数论、算术几何和表示论等专业领域的国际学术，他在这些领域作出了贡献，并对相关领域的学术研究产生了深远影响。Kudla的学术成就获得了学术界的普遍认可。2000年，因其在数论研究方面的成就，他被德国马普基金会和洪堡基金会授予Max-Planck-Forschungsprels奖。2002年，他受邀在国际数学家大会作45分钟报告。值其六十周岁生日之际，深受其影。向的诸多学生、同侪及同行合力出版此纪念文集来表达对Kudla教授的崇敬之情。《算术几何与自守形式》汇集了作者们在Kudla教授多年来关心、研究的领域中的一些结果，包括theta和算术theta提升、Siegel-Weil和算术Siegel-Well公式、Shimura蔟及自守形式方面的重要文章。《算术几何与自守形式》不仅对Kudla教授多年来所悉心研究的学术领域的现状进行了阐述，更为此领域今后的研究指明了

This time of writing is the hundredth anniversary of the publication (1892) of Poincare's first note on topology, which arguably marks the beginning of the subject of algebraic, or "binatorial," topology. There was earlier scattered work by Euler, Listing (who coined the word "topology"), M/Sbius and hiand, Riemann, Klein, and Betti. Indeed, even as early as 1679, Leibniz indicated the desirability of creating a geometry of the topological type. The establishment of topology (or "analysis situs" as it was often called at the time) as a coherent theory, however, belongs to Poincar6. Curiously, the beginning of general topology, also called "point set topology," dates fourteen years later when Fr6chet published the first abstract treatment of the subject in 1906. Since the beginning of time, or at least the era of A'rchimedes, smooth manifolds (curves, surfaces, mechanical configurations, the universe) have been a central focus in mathematics. They have alwayeen at the core of interest in topology

《辛几何讲义》是美国著名数学家shlomosternberg于2010年在清华大学教授辛几何的讲义，分为两个部分。部分(章～0章)介绍了辛群、辛范畴、辛流形和kostant-souriau定理等内容；第二部分(1章～6章)分别讨论了marle常秩嵌入定理、环面作用的凸性定理、hamiltonian线性化定理和极小偶对。 《辛几何讲义》可供从事辛几何和微分几何相关领域研究的学者参考，也可作为高年级本科生和研究生的教材和参考书。

本书系根据苏联国营技术理论书籍出版社出版的楚倍尔毕雷尔著的 本书共分四编 本书适合高等工业学校

Geometric Analysis bines differential equations and differential geometry. An important aspect is to solve geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Ampere equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications. This handbook of geometric analysis provides introductions to and surveys of important topics in geometric analysis and their applications to related fields which is intend to be referred by graduate students and researchers in related areas.

his book is the English version of the French “Geometrie non mutative” published by InterEditions Paris （1990）. After the excellent initial translation by S.K. Berberian, a considerable amount of rewriting was done and many additions made, multiplying by 3.8 the size of the original manuscript. In particular the present text contains several unpublished results.

《罗巴切夫斯基几何学初步》共有12章，分别为：平面几何学的公理、几何学的补充定理、罗巴切夫斯基几何学的基本定理、多边形的角欠和面积、罗巴切夫斯基平面上的基本曲线、空间几何学、罗巴切夫斯基的空间几何学、极限球面上的几何学、指数函数和双曲函数、双曲三角形、罗氏几何学的相容性、罗巴切夫斯基几何学与现代数学。

本书是一部非常好的学习代数曲面的书，提供了复曲面分类的复解析方法。此书是从复代数几何角度研究复曲面的大全类书籍，从初等入门到高深前沿都有涉及。这本书是经典中的经典，讲的是代数曲面的各种专题，每个章节都写的无限。内容包括曲面里的曲线，相交数，霍奇分解，pojectivity，有理曲面分类，Kodaira分类，general曲面，K3&Enrique曲面。此书新版的最后两章写的尤其好，一是 K3 曲面；另一个是 Doanaldson 和Seiber Witten理论，后者是来自模空间的不变量理论，都是现在热门的专题。有位读者这么说：“可以说如果学代数几何没念过这本书，甚至是学几何没念过《紧复曲面(第2版)》，可以考虑换行，是百年难得一见的好书。“可见《紧复曲面(第2版)》书在该领域具有举足轻重的地位。

丢番图问题主要从代数几何进行考虑。书中涵盖了一些研究该课题的基础方法，如高度理论， Néron函数及其在一些经典定理中的应用，如Mordell-Weil 定理、关于积分点的西格尔定理、希尔伯特的不可约定理、Roth定理及其他。该书取代了 Diophantine Geometry,涵盖了许多重要的新资料，如Néron函数理论及Tate和 Silverman的研究结果。目次：值；值的恰当集

《立体几何中的三视图》共11讲,系统的讲述了直观图、三视图。内容包括作图的基本知识、常用的几何作图方法、基本几何体及其直观图的作法、正投影及三视图、点线面的投影、基本几何体的三视图、物体的表面交线、简单组合体三视图的画法、怎样由视图想象出其实物的形状、徒手画图、高考热点--三视图。 《立体几何中的三视图》取材适中，注重观察能力、形象思维能力和空间想象能力的培养，突出方法，结构紧凑，表述清楚，易教易学。 《立体几何中的三视图》可作为高等师范院校数学与应用数学专业教材及中学数学新课程教师培训教材，也可作为中学数学教师教学参考用书。对几何爱好者来讲，也同样是一本有益的读物。

《大学几何学》是一部久负盛名的欧氏几何学名著。 书中的部分强调作图问题，继之概括论述了相似和位似、三角形和四边形的性质，以及调和分割。随后的章节研究了包括反演点、正交圆、共轴圆及阿波罗尼斯圆等内容的圆的几何学。三角形几何学集中讨论了莱莫恩几何和布洛卡几何、等角共轭线、塔克圆以及垂极点，贯穿全书还给出了大量不同难度的习题。 《大学几何学》适合大、中学师生以及几何爱好者学习和研究。

J-全纯曲线理论自其由Gromov于1985年引入以来，已经变得非常重要。在数学中，它的应用包括许多辛拓扑中的关键结果。它也是创立Floer同调的主要灵感之一。在数学物理中，它提供了一个自然的语境用以在其中定义镜像对称猜想的两个重要成分-Gromov-Witten不变量和量子上同调。《美国数学会经典影印系列：J-全纯曲线和辛拓扑（第2版 ）》的主要目的是以充分和严格的细节来建立这个主题的基本定理。特别地，《美国数学会经典影印系列：J-全纯曲线和辛拓扑（第2版 ）》包含关于球面的Gromov紧性定理、球面的黏合定理以及在半正情形下量子乘法的结合性的完整的证明。《美国数学会经典影印系列：J-全纯曲线和辛拓扑（第2版 ）》也可以作为对辛拓扑当前工作的介绍：有两个关于应用的长的章节，一章专注于辛拓扑的经典结果，另一章涉及量子上同调。最后一章概述了

19世纪下半叶至20世纪初，欧氏几何学经历了一场快速的复兴，期间发现了数以千百计的新定理。本书分十三个章节介绍了其中优美的一些珍宝。有一些构思精妙的定理在别的书中很难看到，如亚当斯圆，里格比点，春木定理等。 本书写的生动有趣，逻辑严谨，深入浅出。书中所列举的定理基本上都给出了详细的初等证明，书末附有习题解答。具有中学几何基本知识的读者就能看懂。

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the relations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory,simplicial plexes, singular theory, axiomatic homology, differential topology, etc.), we concentrate our attention on concrete problems in low dimensions, introducing only as much algebraic machinery as necessary for the problems we meet. This makes it possible to see a.wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to bee practicing algebraic topologists--without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical development of the subject.

《复杂曲面数字化制造的几何学理论和方法》系统地总结了作者丁汉，朱利民在复杂曲面数字化制造基础理论方面的研究成果。全书共7章，～4章为几何学基础，沿着曲线、曲面论→曲面上的几何学→高维微分几何→Lie群、Lie代数的线路循序渐进地介绍了现代微分几何和运动学的基础理论、内在联系及统一分析方法，并结合应用穿插介绍了一些外的成果。第5～7章以微分几何和化为工具，介绍了作者提出的曲面测量、加工和夹持定位的新原理和新方法，具体内容包括：点一曲面法向误差函数的可微性条件及其二阶导数的解析计算方法，散乱点云曲面逼近的统一方法体系，回转刀具扫掠包络面的解析表达、局部重建与整体形状控制原理，自由曲面线接触和高阶点接触数控加工刀位规划理论和方法，刀具全局可达方向锥的GPU计算方法，夹持完全约束性判别和夹具定位误差