Week 43

Today I finished chapter 4 and just started chapter 5.  Chapter 3 studied surfaces topologically and in chapter 4 we gave examples on how to put the simplest and most uniform geometric structure on surfaces.  Chapter 5 contains the most general theory.  It builds heavily on the tools of differential calculus, extended to abstract surfaces.  The basic constructions needed for this extension are contained in section 5.1, and it is important that you make an effort to understand this from the beginning.

A small remark on the mandatory problem set:  due to a typo there is no problem 5.