《环与代数》主要介绍国内外环与代数的最新研究成果和发展方向，在第一版的基础上，除删除了一些陈旧内容外，还增添关于分次环、路代数、箭图表示、有限表示型箭图4章，力图向读者介绍分次环、箭图及其表示最基本的知识，使之能够了解和进入环与代数当前研究的一些非常具有活力的领域。我们将介绍分次环、分次模、分次Artin环、Smash积、分次本原环、箭图的路代数、路代数的性质、路代数的张量积和箭图的直积；箭图表示的基本内容、箭图表示的Auslander-Reiten理论；Dynkin图及其表示，Betaastein-Gelfand-Ponomarev反射函子，有限表示型的箭图的刻画（Gabriel定理）等内容。《环与代数》适合数学及相关专业高年级大学生、研究生、教师及科研人员阅读参考。

This book is a survey of the most important directions of research in transcendental number theory. The central topics in this theory include proofs of irrationality and transcendence of various numbers，especially those，that arise as the values of special functions. Questions of this sort go back to ancient times. An example is the old problem of squaring the circle，which Lindemann showed to bc impossible in 1882，when hc proved that Pi is a trandental number. Euler's conjecture that the logarithm of an algebraic number to an algebraic base is transcendental was included in Hilbert's famous list of open problems; this conjecture was proved by Gel'fond and Schneider in 1934. A more recent result was Anerv's surprising proof of the irrationality of ξ（3）in 1979.The quantitative aspects of the theory have important applications to the study of Diophantine equations and other areas of number theory. For a reader interested in different branches of number theory，this monograph provides both an overview of the central ideas and techniques of transcendental number theory，and also a guide to the most important results and references.

《概率论与数理统计》共有9章，分别介绍了随机事件与概率、随机变量及其分布、随机变量的数字特征、多维随机变量及其分布、大数定律与中心极限定理、数理统计的基本概念、参数估计、假设检验、回归分析及方差分析。每章最后都有一节介绍综合例题。每节都有相当数量的习题，每章末附有复习题，书末附有部分习题答案。《概率论与数理统计》可作为高等院校工科、理科（非数学专业）以及其他各相关专业的概率论与数理统计课程的教材，也可作为工程技术人员等实际工作者的自学用书。

本书内容由随机事件及其概率、随机变量及其分布、随机向量、随机变量的数字特征、大数定律与中心极限定理。数理统计的基本知识、参数估计、假设检验，方差分析与回归分析、Mathemafica软件应用、常见。的概率论与数理统计模型11章构成。随各章内容配有一定数量的习题，书末附有习题选解与提示及6种附表以备查用。编写中始终以强化理论学习为基础，以应用为目的，力求做到深入浅出、通俗易懂、便于自学、提高成效。本书可作为高等院校理工科、经济学、管理学等各专业概率论与数理统计课程的教材，也可作为教师、学生和科技工作者学习概率论与数理统计知识的参考书。

Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics， and its contemporary applications are many and diverse. This modern approach to homological algebra， by two leading writers in the field， is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory （sheaf cohomology， spectral sequences， etc.） are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

This book contains two contributions on closely related subjects： the theory of linear algebraic groups and invariant theory. The first part is written by T. A. Springer， a well-known expert in the first mentioned field. Hc presents a comprehensive survey， which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields （finite， local， and global）. The authors of part two-E. B. Vinbcrg and V. L. Popov-arc among the most active researchers in invariant theory. The last 20 years have bccn a period of vigorous development in this field duc to the influence of modern methods from algebraic geometry. The book will bc very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.

The first part of this book on Discrete Subgroups of Lie Groups is written by E.B. Vinberg， V.V. Gorbatsevich， and O.V. Shvartsman. Various types of discrete subgroups of Lie groups arise in the theory of functions of complex variables， arithmetic， geometry， and crystallography. Since the foundation of their general theory in the 50-60s of this century， considerable and in many respects exhaustive results were obtained. This development is reflected in this survey. Both semisimple and general Lie groups are considered. Part II on Cohomologies of Lie Groups and Lie Algebras is written by B.L. Feigin and D.B. Fuchs. It contains different definitions ofcohomologies of Lie groups and （both finite-dimensional and some infinite-dimensional）Lie algebras， the main methods of their calculation， and the results of these calculations. The book can be useful as a reference and research guide to graduate students and researchers in different areas of mathematics and theoretical physics.

The aim of this survey， written by V. A. lskovskikh and Yu. G.Prokhorov， is to provide an exposition of the structure theory of Fano varieties， i.e. algebraic varieties with an ample anticanonical divisor.Such varieties naturally appear in the birational classification of varieties of negative Kodaira dimension， and they are very close to rational ones. This EMS volume covers different approaches to the classification of Fano varieties such as the classical Fanolskovskikh"double projection"method and its modifications，the vector bundles method due to S. Mukai， and the method of extremal rays. The authors discuss uniruledness and rational connectedness as well as recent progress in rationality problems of Fano varieties. The appendix contains tables of some classes of Fano varieties.This book will be very useful as a reference and research guide for researchers and graduate students in algebraic geometry.

The book by Gorbatsevich， Onishchik and Vinberg is the first volume in a subseries of the Encyclopaedia devoted to the theory of Lie groups and Lie algebras.The first part of the book deals with the foundations of the theory based on the classical global approach of Chevalley followed by an exposition of the alternative approach via the universal enveloping algebra and the Campbell-Hausdorff formula. It also contains a survey of certain generalizations of Lie groups.The second more advanced part treats the topic of Lie transformation groups covering e.g. properties of orbits and stabilizers，homogeneous fibre bundles， Frobenius duality， groups of automorphisms of geometric structures， Lie algebras of vector fields and the existence of slices. The work of the last decades including the most recent research results is covered.The book contains numerous examples and describes connections with topology， differential geometry， analysis and applications. It is written for graduate students and researchers in mathematics and theoretical physics.

The book contains a comprehensive account of the structure and classification of Lie groups and finite-dimensional Lie algebras （including semisimple，solvable，and of general type）. In particular，a modem approach to the description of automorphisms and gradings of semisimple Lie algebras is given. A special chapter is devoted to models of the exceptional Lie algebras. The book contains many tables and will serve as a reference. At the same time many results are accompanied by short proofs.Onishchik and Vinberg are internationally known specialists in their field; they are also well known for their monograph“Lie Groups and Algebraic Groups”（Springer-Verlag 1990）.The book will be immensely useful to graduate students in differential geometry，algebra and theoretical physics.