What next?

I've finished singe variable calculus and I want a taste of pure mathematics before I go to university next September. I'm going to get a grasp of sets and proof first but what next? Number theory, analysis or what? Book recommendations would be ideal!

If I need a toilet installed, I call a plumber.  If I needed a sewer network, I'd call an engineer.  If I need an inscrutable process examined for manipulatable numbers, I call a mathematician.

The thing is, I can install my own toilet, -and- I can manipulate my own equations, but I cannot install a sewer network.