NTRODUCTION
CHAPTER I THE FIVE GROUPS OF AXIOMS
1.The elements of geometry and the five groups of axioms
2.Group I.Axioms of connection.
3.Group II.Axioms of order .
4.Consequences of the axioms of connection and order
5.Group III.Axiom of parallels（Euclid's axiom）
6.Group IV.Axioms of congruence .
7.Consequences of the axioms of congruence
8.Group V.Axiom of continuity （Archimedes's axiom）
CHAPTER II COMPATIBILITY AND MUTUAL INDEPENDENCE OF THE AXIOMS
9. Compatibility of the axioms
10.Independence of the axioms of parallels （Non-euclidean geom-etry）
11.Independence of the axioms of congruence
12.Independence of the axiom of continuity（Non-archimedean geometry）
CHAPTER III THE THEORY OF PROPORTION
13. Complex number systems
……
