对称

1.MetricSpacesandtheirGroups

1.1MetricSpaces

1.2Isometries

1.3IsometriesoftheRealLine

1.4MattersArising

1.5SymmetryGroups

2.IsometriesofthePlane

2.1CongruentTriangles

2.2IsometriesofDifferentTypes

2.3TheNormalFormTheorem

2.4ConjugationofIsometries

3.SomeBasicGroupTheory

3.1Groups

3.2Subgroups

3.3FactorGroups

3.4SemidirectProducts

4.ProductsofReflections

4.1TheProductofTwoReflections

4.2ThreeReflections

4.3FourorMore

5.GeneratorsandRelations

5.1Examples

5.2SemidirectProductsAgain

5.3ChangeofPresentation

5.4TriangleGroups

5.5AbelianGroups

6.DiscreteSubgroupsoftheEuclideanGroup

6.1LeonardosTheorem

6.2ATrichotomy

6.3FriezesandTheirGroups

6.4TheClassification

7.PlaneCrystallographicGroups：OPCase

7.1TheCrystallographicRestriction

7.2TheParametern

7.3TheChoiceofb

7.4Conclusion

8.PlaneCrystallographicGroups：ORCase

8.1AUsefulDichotomy

8.2TheCasen=1

8.3TheCasen=2

8.4TheCasen=4

8.5TheCasen=3

8.6TheCasen-6

9.TessellationsofthePlane

9.1RegularTessellations

9.2Descendantsof（4，4）

9.3Bricks

9.4SplitBricks

9.5Descendantsof（3，6）

10.TessellationsoftheSphere

10.1SphericalGeometry

10.2TheSphericalExcess

10.3TessellationsoftheSphere

10.4ThePlatonicSolids

10.5SymmetryGroups

11.TriangleGroups

11.1TheEuclideanCase

11.2TheEllipticCase

11.3TheHyperbolicCase

11.4CoxeterGroups

12.RegularPolytopes

12.1TheStandardExamples

12.2TheExceptionalTypesinDimensionFour

12.3ThreeConceptsandaTheorem

12.4SchlaflisTheorem

Solutions

GuidetotheLiterature

Bibliography

IndexofNotation

Index

本书以通俗易懂的方式讲述几何与群的本质，以及两者问的联系（即对称），并且自然地延伸到一些高级的观点和材料（如有限和仿射Coxeter群，这是李群李代数以及Kac—Moody代数的基础；球面的分割，这是球面几何的内容；上半平面被群SL2（z）的作用，这是双曲几何与自守函数的基础）。阅读本书所需的几何与群的知识在书中均有通俗易懂的介绍（附有大量几何直观图形）。 本书是一本优秀的数学教材，适用于数学系本科生和其他专业对数学有兴趣的本科生用作数学参考书或课外读物。