Vaughn Climenhaga

Associate Professor
Department of Mathematics
University of Houston

In Fall 2007 I was the TA for a MASS course taught by Anatole Katok under the title "Surfaces: (almost) everything you wanted to know about them."  From that experience was born a set of course notes, which after some extensive polishing and reworking was published in book form by the American Mathematical Society.  The initial draft is still posted on the course website, with all its errors, omissions, and countless rough spots which were smoothed out for the book itself (along with all those which weren't).

Prof. Katok has a website with more information about the book, including excerpts.  The book has now been published, and is available through the AMS, and of course through places like Amazon.

Proving that the
                        area of a spherical triangle is proportional to
                        its angular excess