本书为第三版，继前两版之后，接着探讨“如何最有效地将大量等球放入n维的欧氏空间中？”这一核心问题。同时，作者仍在思考一些相关的问题，如：吻接数问题，覆盖问题，量子化问题以及格分类与二次型。与前两版相同的是，第三版也描述了以上这些问题与数学或自然科学中其他一些领域的联系，这些领域包括：码理论，数字通信，数论，群论，模拟数字转换以及数据压缩与n维晶体。值得特别注意的是，本书收录了一篇介绍本领域的最新的一些研究成果的报告，并补充了1988-1998年间出版的超过800项的参考书目，相信这些珍贵的资料一定能够引起读者特殊的兴趣。

本书适用于数学专业的高年级本科生或研究生以及需要相关知识的科研人员。

Preface to First Edition

Preface to Third Edition

List of Symbols

Chapter 1 Sphere Packings and Kissing Numbers

Chapter 2 Coverings,Lattices and Quantizers

Chapter 3 Codes,Designs and Groups

Chapter 4 Certain Important Lattices and Their Properties

Chapter 5 Sphere Packing and Error-Correcting Codes

Chapter 6 Laminated Lattices

Chapter 7 Further Connections Betwwen Codes and Lattices

Chapter 8 Algebraic Constructions for Lattices

Chapter 9 Bounds for Codes and Sphere Packings

Chapter 10 Three Lectures on Exceptional Groups

Chapter 11 The Golay Codes and the Mathieu Groups

Chapter 12 A Characterization of the Leech Lattice

Chapter 13 Bounds on Kissing Numbers

Chapter 14 Uniqueness of Certain Spherical Codes

Chapter 15 On the Classification of Integral Quadratic Forms

Chapter 16 Enumeration of Unimodular Lattices

Chapter 17 The 24-Dimensional Odd Unimodular Lattices

Chapter 18 Even Unimodular 24-Dimensional Lattices

Chapter 19 Enumeration of Extremal Self-Dual Lattices

Chapter 20 Finding the Closest Lattice Point

Chapter 21 Voronoi Cells of Lattices and Quantization Errors

Chapter 22 A Bound for the Covering Radius of the Leech Lattice

Chapter 23 The Covering Radius of the Leech Lattice

Chapter 24 Twenty-Three Constructions for the Leech Lattice

Chapter 25 The Cellular Structure of the Leech Lattice

Chapter 26 Lorentzian Forms for the Leech Lattice

Chapter 27 The Automorphism Group of the 26-Dimensional Even Unimodular Lorentzian Lattice

Chapter 28 Leech Roots and Vinberg Groups

Chapter 29 The Monster Group and its 196884-Dimensional Space

Chapter 30 A Monster Lie Algebra?

Bibliography

Supplementary Bibliography

Index