You leave quite a few restrictions. You don't have books, can't get books, and can't use the internet much. So, there isn't really much for us to tell you. You HAVE to have some form of book. You can't learn from nothing but a list of a few theorems. So, it seems the least restrictive of your list is the internet. Obviously, you can use it some.
By the way, you can't just learn the most important theorems. The rest of the stuff in the book leads up to these theorems and the theorems make no sense, or can not be proven, unless you have all the rest.
This should get you a lot of the basics. But, it's on the internet. As I said before, you basically left no possibilities for help, so I have to delete one of your restrictions.
Other than that, search for undergraduate abstract algebra online. "Intro" or "elementary" are words that tell you it's going to be undergrad level. Here are lecture notes from Hungerford's undergrad book, which is the book I used as an undergrad. If you could at least print this off, or something like it, that would solve the internet access problem.