I was interested in figuring out when the next pass of the ISS was going to occur, and was reminded of the interesting mathematics involved in predicting satellite orbits. While I’ll probably never use this, the code that everyone uses are derived from the original FORTRAN code, generally referred to as the NORAD SGP4 and SDP4 models. You can find these, as well as more modern revisions to fix bugs in the original codes at the Celestrak website.
Addendum: The original Spacetrack Report #3 linked to by Celestrak seemed to be trashed. Luckily, you can get a good copy from the Amsat website.