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.
This is a good introduction, written at the undergraduate level.
Great book by a great mathematician. A work of philosophy as well as mathematics.
A very interesting discussion about the nature of mathematical discovery and the search for absolute truth, written by a philosophical skeptic.
These notes will be useful when we get to the last part of the course, in which we construct hyperbolic geometry, whose very existence shows that the Euclidean Parallel Postulate cannot be proved from Hilbert's axioms plus Dedekind's Axiom.
Of course, this is our textbook, but it also contains a very useful bibliography that I highly recommend for further reading.
A very nice discussion of several topics that we will not treat in the course, including ruler and compass constructions.
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.