Lecture Notes

You can find the lecture notes here:


They were written by José Mourão, José Natário and João Pimentel Nunes, the original designers of this course. José Natário's website includes some nice resources:



  • Chapter 2, all sections;
  • Chapter 3, Sections 3.1.3 and 3.1.4 on topological spaces, Sections 3.2.1 and 3.2.2 on manifolds;
  • Chapter 4, Section 4.1 and parts of Sections 4.2 and 4.3.
Please see the summaries for full details on coverage, especially for the later lectures.