LATEX
LATEX is a typesetting language capable of easily incorporating non-alphanumeric symbols. Its primary use is in academia by those pursuing symbol-laden subjects, e.g. logic, philosophy, mathematics, computer science, and the hard sciences. In happy news, LATEX editors are usually open source, so you won't need to purchase anything. In less happy news, LATEX is a markup language (like html) which means there's a substantial learning curve for those who have never done any programming. If you're planning to pursue graduate-level study (or really, really want typed notes as an undergraduate) in one of the subjects listed above, it's probably worth your time to learn; if not, I wouldn't recommend bothering. To give you a better idea of what's entailed, I've attached a screen shot of a random page in my notes side-by-side with the LATEX input:
If you'd still like to learn, go ahead and install a LATEX distribution; I'd recommend MikTeX for Windows users and MacTeX for Mac users. Both are free and come with a built-in editor (TeXWorks and TeXShop respectively). For MikTeX, you'll want to allow it to download packages on the fly. Next, download and open (in your LATEX editor) this document and get comfortable with the basics; afterwards, take a look at this for some slightly more complicated constructions. If for some reason you don't like either of the included editors, Wikipedia maintains a page comparing alternatives.