1. Classical notions and definitions -- 2. On integer geometry -- 3. Geometry of regular continued fractions -- 4. Complete invariant of integer angles -- 5. Integer trigonometry for integer angles -- 6. Integer angles of integer triangles -- 7. Continued fractions and SL(2; Z) conjugacy classes. Elements of Gauss reduction theory. Markoff spectrum -- 8. Lagrange's theorem -- 9. Gauss-Kuzmin statistics -- 10. Geometric aspects of approximation -- 11. Geometry of continued fractions with real elements and the second Kepler's law -- 12. Extended integer angles and their summation -- 13. Integer angles of polygons and global relations for toric singularities -- 14. Basic notions and definitions of multidimensional integer geometry -- 15. On empty simplices, pyramids, parallelepipeds -- 16. Multidimensional continued fractions in the sense of Klein -- 17. Dirichlet groups and lattice reduction -- 18. Periodicity of Klein polyhedra. Generalization of Lagrange's theorem -- 19. Multidimensional Gauss-Kuzmin statistics -- 20. On construction of multidimensional continued fractions -- 21. Gauss Reduction in higher dimensions -- 22. Approximation of maximal commutative subgroups -- 23. Other generalizations of continued fractions.