Set Theory

We aren't going to assume much about set theory in this course, but, in case you are curious, here are a few references.

A very brief introduction to naive set theory,
This is a set of notes that I wrote a few years ago to serve as a sort of crib sheet for students who wanted to know what it's about, but don't want to get tangled up in it. This is a .pdf file, so you'll need Acrobat Reader to look at it.
Naive Set Theory, by P. R. Halmos.
This is a good introduction, written at the undergraduate level.
A Mathematical Introduction to Logic, by Y. I. Manin
Great book by a great mathematician. A work of philosophy as well as mathematics.
Proofs and Refutations, I. Lakatos.
A very interesting discussion about the nature of mathematical discovery and the search for absolute truth, written by a philosophical skeptic.

Geometry

Euclidean and Non-Euclidean Geometries, by M. J. Greenberg.
Elementary Geometry from and Advanced Standpoint by E. E. Moise.
A very nice discussion of several topics that we will not treat in the course, including ruler and compass constructions.
The Elements by Euclid.
The best modern translation is by Sir Thomas L. Heath. It's available in three volumes from Dover, with Heath's copious notes about the history of the study of Euclid, problems found with it, proposed solutions, controversies, etc. Fascinating not only for the discussion of the mathematics but for the discussion of the changing perspectives on Euclid throughout the last 2500 years. The closest thing that mathematics has to a canonical text.