brief summary

Part I. Foundations of Mathematics.

Part II. Algebra.

Part III. Number Theory.

Part IV. Geometry.

Part V. Analytic Geometry.

Part VI. Topology.

Part VII. Algebraic Topology.

Part VIII. Analysis.

Part IX. Category Theory.

Part X. Probability and Statistics.

Part XI. Applied Mathematics.

• Chap.1. Mathematical Logic.
• Chap.2. Set Theory.
• Chap.3. Relations and Structures.
• Chap.4. Arithmetic.
• Chap.5. Construction of Number System.
• Chap.6. Algebra.
• Chap.7. Number Theory.
• Chap.8. Geometry.
• Chap.9. Analytic Geometry.
• Chap.10. Topology.
• Chap.11. Topology II.
• Chap.12. Algebraic Topology.
• Chap.13. Algebraic Topology II.
• Chap.14. Real Analysis.
• Chap.15. Differential Calculus.
• Chap.16. Integral Calculus.
• Chap.17. Functional Analysis
• Chap.18. Differential Equations.
• Chap.19. Differential Geometry.
• Chap.20. Function Theory (Complex Analysis).
• Chap.21. Complex Analysis II.
• Chap.22. Areas Involved in Category Theory.
• Chap.23. Category Theory.
• Chap.24. Probability.
• Chap.25. Probability Calculation, Statistics.
• Chap.26. Miscellaneous.
• Chap.27. Optimization.
• Chap.28. Dynamical Systems.

• Appendices: Symbols, Tables.
• Bibliography.
• Index.