"I would really like to learn this stuff". If you are serious:

* Stick with math classes through school. Focus on non-standard math: logics, group theory, meta-mathematics. This will force to thing abstractly.

* Go to college, specialize in software engineering. Take every compiler class you can get.

* Collect/read the standard compiler texts: Aho/Ullman, etc.

* Build a compiler. Start by building a rotten one. This will teach you some issues. Build a second one. Repeat.