线性几何包括仿射几何和射影几何，这部分内容在国内的传统数学教学中长期受到了忽视，然而几何学的重要性已经日趋受人重视。此书融线性代数解析几何为一体，数形结合，更有利于学生弄懂而且弄透。此书内容精练， 习题丰富，很适合数学专业的本科生使用， 为进入现代数学做好铺垫。

Guide to the Reader

Chapter Ⅰ Vector Spaces

 1.1 Sets

 1.2 Groups, Fields and Vector Spaces

 1.3 Subspaces

 1.4 Dimension

 1.5 The Ground Field

Chapter Ⅱ Affine and Projective Geometry

 2.1 Affine Geometries

 2.2 Affine Propositions of Incidence

 2.3 Affine Isomorphisms

 2.4 Homogeneous Vectors

 2.5 Projective Geometrics

 2.6 The Embedding of Affine Geometry in Projective Geometry

 2.7 The Fundamental Incidence Theorems of Projective Geometry

Chapter Ⅲ Isomorphisms

 3.1 Affinities

 3.2 Projectivities

 3.3 Linear Equations

 3.4 Affine and Projective Isomorphisms

 3.5 Semi-linear Isomorphisms

 3.6 Groups of Automorphisms

 3.7 Central Collineations

Chapter Ⅳ Linear Mappings

 4.1 Elementary Properties of Linear Mappings

 4.2 Degenerate Affinities and Projectivities

 4.3 Matrices

 4.4 The Rank of a Linear Mapping

 4.5 Linear Equations

 4.6 Dual Spaces

 4.7 Dualities

 4.8 Dual Geometries

Chapter Ⅴ Bilinear Forms

 5.1 Elementary Properties of Bilinear Forms

 5.2 Orthogonality

 5.3 Symmetric and Alternating Bilinear Forms

 5.4 Structure Theorems

 5.5 Correlations

 5.6 Projective Quadrics

 5.7 Affine Quadrics

 5.8 Sesquilinear Forms

Chapter Ⅵ Euclidean Geometry

 6.1 Distances and Euclidean Geometries

 6.2 Similarity Euclidean Geometries

 6.3 Euclidean Quadrics

 6.4 Euclidean Automorphisms

 6.5 Hilbert Spaces

Chapter Ⅶ Modules

 7.1 Rings and Modules

 7.2 Submodules and Homomorphisms

 7.3 Direct Decompositions

 7.4 Equivalence of Matrices over F[X]

 7.5 Similarity of Matrices over F

 7.6 Classification of Coilineations

Solutions

List of Symbols

Bibliography

Index