在几何学方面，本书介绍了射影平面中的坐标，并将坐标的性质与某些自同构的可传递性性质联系起来，进一步探讨了这些自同构。书中详细研究了八元数平面，并在一个允许非除法坐标的几何背景下进行了讨论。该背景的公理化版本也得到了介绍。最后，本书概述了非结合代数与其他几何结构（包括建筑）的联系。 在代数学方面，本书推导了交替代数的基本性质，包括公理化的维度发展、二次型的基础理论、齐次映射及其极化的处理，并研究了组合代数上的厄米矩阵的范数形式。 本书适合高年级本科生和研究生阅读。

前辅文
Introduction
Chapter 1. Affine and Projective Planes
  §1.1. Preview
  §1.2. Incidence geometry
  §1.3. Affine planes
  §1.4. Projective planes
  §1.5. Duality
  §1.6. Exercises
Chapter 2. Central Automorphisms of Projective Planes
  §2.1. Preview
  §2.2. Projections and automorphisms
  §2.3. Transvections and dilatations
  §2.4. Transitivity properties
  §2.5. Exercises
Chapter 3. Coordinates for Projective Planes
  §3.1. Preview
  §3.2. Ternary systems
  §3.3. Two coordinatizations related to G(C)
  §3.4. Transvections and algebraic properties
  §3.5. Exercises
Chapter 4. Alternative Rings
  §4.1. Preview
  §4.2. Left Moufang rings
  §4.3. Artin’s Theorem
  §4.4. Inverses in alternative rings
  §4.5. The Cayley-Dickson process
  §4.6. Composition algebras
  §4.7. Split and division composition algebras
  §4.8. Exercises
Chapter 5. Configuration Conditions
  §5.1. Preview
  §5.2. Desargues condition
  §5.3. Quadrangle sections
  §5.4. Pappus condition
  §5.5. Configurations and central automorphisms
  §5.6. Exercises
Chapter 6. Dimension Theory
  §6.1. Preview
  §6.2. Dimensionable sets
  §6.3. Independence and bases
  §6.4. Strongly dimensionable sets
  §6.5. Exercises
Chapter 7. Projective Geometries
  §7.1. Preview
  §7.2. Projective and nearly projective geometries
  §7.3. Relation to strongly dimensionable sets
  §7.4. Classification of projective geometries
  §7.5. Exercises
Chapter 8. Automorphisms of G(V)
  §8.1. Preview
  §8.2. The Fundamental Theorem
  §8.3. Subgroups of Aut(G(V ))
  §8.4. Simple groups
  §8.5. Exercises
Chapter 9. Quadratic Forms and Orthogonal Groups
  §9.1. Preview
  §9.2. Quadratic forms
  §9.3. Orthogonal groups
  §9.4. Exercises
Chapter 10. Homogeneous Maps
  §10.1. Preview
  §10.2. Polarization of homogeneous maps
  §10.3. Exercises
Chapter 11. Norms and Hermitian Matrices
  §11.1. Preview
  §11.2. Hermitian matrices and HEn(C)
  §11.3. Norms on H(Cn)
  §11.4. Transitivity of HEn(C)
  §11.5. Trace and adjoint
  §11.6. H(C3)
  §11.7. Exercises
Chapter 12. Octonion Planes
  §12.1. Preview
  §12.2. The construction of octonion planes
  §12.3. Simplicity of PHE3(O)
  §12.4. Automorphisms of octonion planes
  §12.5. Exercises
Chapter 13. Projective Remoteness Planes
  §13.1. Preview
  §13.2. Definition and examples
  §13.3. Groups of Steinberg type
  §13.4. Transvections
  §13.5. Exercises
Chapter 14. Other Geometries
  §14.1. Preview
  §14.2. Erlangen program
  §14.3. The geometry of R-spaces
  §14.4. Buildings
  §14.5. Generalized n-gons
  §14.6. Moufang sets and structurable algebras
  §14.7. Freudenthal-Tits magic square
  §14.8. Exercises
Bibliography
Index