chapter 1. euclid''s geometry
1. a first look at euclid''s elements
2. ruler and compass constructions
3. euclid''s axiomatic method
4. construction of the regular pentagon
5. some newer results
chapter 2. hilbert''s axioms
6. axioms of incidence
7. axioms of betweenness
8. axioms of congruence for line segments
9. axioms of congruence for angles
10. hilbert planes
11. intersection of lines and circles
12. euclidean planes
chapter 3. geometry over fields
13. the real cartesian plane
14. abstract fields and incidence
15. ordered fields and betweenness
16. congruence of segments and angles
17. rigid motions and sas
18. non-archimedean geometry
chapter 4. segment arithmetic
19. addition and multiplication of line segments
20. similar triangles
21. introduction of coordinates
chapter 5. area
22. area in euclid''s geometry
23. measure of area functions
24. dissection
25. quadrature circuli
26. euclid''s theory of volume
27. hilbert''s third problem
chapter 6. construction problems and field extensions
28. three famous problems
29. the regular 17-sided polygon
30. constructions with compass and marked ruler
31. cubic and quartic equations
32. appendix: finite field extensions
chapter 7. non-euclidean geometry
33. history of the parallel postulate
34. neutral geometry
35. archimedean neutral geometry
36. non-euclidean area
37. circular inversion
38. digression: circles determined by three conditions
39. the poincare model
40. hyperbolic geometry
41. hilbert''s arithmetic of ends
42. hyperbolic trigonometry
43. characterization of hilbert planes
chapter 8. polyhedra
44. the five regular solids
45. euler''s and cauchy''s theorems
46. semiregular and face-regular polyhedra
47. symmetry groups of polyhedra
appendix: brief euclid
notes
references
list of axioms
index of euclid''s propositions
index
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