1. Topological spaces 2. Neighborhoods 3. Interior of a set and adherence of a set 4. Subspaces 5. Continuous functions 6 Initial topologies, 7. Product spaces 8.Further results concerning continuous functions 9. Compact spaces, 10. Locally compact spaces 11. Connect spaces 12. Final topologies quotient spaces 13. Metrics metric spaces 14. Sequences 15. Complete metric spaces 16. Compact metrizable spaces 17. Uniformly continuons functions 18. Normed spaces 19. The stone weierstrass theorem 20. Normal spaces 21.Partions of unity 22. Baire spaces, 23. Filters limits nets notations and terminology 24. Uniform structure uniform spaces 25. Semi metric and uniforms spaces 26. complete uniform spaces, uniform continuous functions. 27. Uniformly continuous functions 28. Isomorphisms completion of uniforms spaces 29. Uniformizable spaces completely regular spaces