The following books by I. M. Gelfand are interesting:
Algebra
Trigonometry
The Method of Coordinates
Functions and Graphs
There's also this gem by George Birkhoff:
Basic Geometry
They are written so as to build intuition and get a feeling for what's going on behind the scenes. If you are interesting in delving a little deeper than usual high school topics, then I'd suggest these books too:
How to Prove It - Daniel Velleman
How to Think Like a Mathematician - Kevin Houston
'How to Prove It' is an all time favorite everyone. The second is more of a personal recommendation: I discovered it when I entered university and appreciated it very much. I think the informal discussions and insights it gives are valuable.
There are more references but they depend on what is your purpose: competitions, bridging your way into higher abstract mathematics, etc.