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CHAPTER ISummary of Main Results1. Generalized Jacobians2. Abelian coverings3. Other resultsBibliographic noteCHAPTER IIAlgebraic Curves

Up until recently， Riemannian geometry and basic topology were not included， even by departments or faculties of mathematics， as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead （and still are given in some places） gradually came to be viewed as anachronisms. However， there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date， that is to say，which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education， and what might be the appropriate level of abstractness of their exposition The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that， in addition to the geometry，of curves and surfaces， the following topics are certainly useful in the various areas of application of mathematics （especially in elasticity and relativity，to name but two）， and are therefore essential： the theory of tensors （including eovariant differentiation of them）; Riemannian curvature;

This book is devoted to explaining a wide range of applications of continuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods， organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems.本书为英文版。

土地管理法制化，是我国“依法治国”方略的重要组成部分。为了科学合理地利用土地，切实保护耕地，促进社会经济的可持续发展，必须把土地规划、利用、保护、监督等各项管理活动纳入法治的轨道。纵观这部试用教材，有以下几个特点：1．以土地基本国情为起点，以“十分珍惜、合理利用土地，切实保护耕地”的基本国策为指导，比较全面、准确地介绍了我国现行土地政策、法律、法规、规章的基本内容。2．坚持了理论联系实际的学风，突出实用性。既注重对土地法基本理论、基本规则的介绍，又注意吸收本学科最新且比较成熟的研究成果。3．教材中适当增加了土地行政法方面的内容，这正是“依法治国”宪法原则的基本要求，很有必要。因“依法治国”的核心是“依法行政”，所以，努力提高各级人民政府地政部门及其公职人员依法行政的水平，是实现土地管理法制化的关键所在。我们相信该试用教材对大学土地资源管理及相近专业的师生、土地管理工作者学习了解我国现行土地政策与法规，能有重要的参考价值，同时对加快我国土地管理法制化的进程也能起到一定的助推作用。

This book is intended for the young student who is interested in graph theory and wishes to study it as part of his mathematical education. Experience at Cambridge shows that none of the currently available texts meet this need. Either they are too specialized for their audience or they lack the depth and development needed to reveal the nature of the subject.本书为英文版。

The guiding principle in this book is to use differential forms as an aid in exploring some of the less digestible aspects of algebraic topology. Accordingly， we move primarily in the realm of smooth manifolds and use the de Rham theory as a prototype of all of cohomology. For applications to homotopy theory we also discuss by way of analogy cohomology with arbitrary coefficients. Although we have in mind an audience with prior exposure to algebraic or differential topology， for the most part a good knowledge of linear algebra， advanced calculus， and point-set topology should suffice. Some acquaintance with manifolds， simplicial complexes， singular homology and cohomology， and homotopy groups is helpful， but not really necessary. Within the text itself we have stated with care the more advanced results that are needed， so that a mathematically mature reader who accepts these background materials on faith should be able to read the entire book with the minimal prerequisites.本书为英文版。

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。

In expositions of the elements of topology it is customary for homology to be given a fundamental role. Since Poincare， who laid the foundations of topology， homology theory has been regarded as the appropriate primary basis for an introduction to the methods of algebraic topology. From homotopy theory， on the other hand， only the fundamental group and covering-space theory have traditionally been included among the basic initial concepts. Essentially all elementary classical textbooks of topology （the best of which is， in the opinion of the present authors， Seifert and Threlfall's A Textbook of Topology） begin with the homology theory of one or another classof complexes. Only at a later stage （and then still from a homological point of view） do fibre-space theory and the general problem of classifying homotopy classes of maps （homotopy theory） come in for consideration. However， methods developed in investigating the topology of differentiable manifolds， and intensively elaborated from the 1930s onwards （by Whitney and others）， now permit a wholesale reorganization of the standard exposition Of the fundamentals of modern topology. In this new approach， which resembles more that of classical analysis， these fundamentals turn out to consist primarily of the elementary theory of smooth manifolds， homotopy theory based on these， and smooth fibre spaces. Furthermore， over the decade of the 1970s it became clear that exactly this complex of topological ideas and methods were proving to be fundamentally applicable in various areas of modern physics.本书为英文版。

A revolution occurred quietly in teh development of physics-or，more accu-rately，of science-in the last three decades.The revolution touches uponevery discipline in both the natural and social sciences.We are referring to the birth of a new science-nonlinear science-which，for the sake of presenta-tion，may be diveded into six parts：fractals，chaos，pattrn formation，sol-itons，cellular automata，and complex systems.本书为英文版！