At the risk of sounding like some old fashioned dude i would like to say that subjects like group theory, differential geometry, etc cannot be learned from looking at websites. For example, although the mathworld site is a reliable source it is far from introductory. This site gives the complete mathematical formalism behind the concepts it likes to explain, but it does NOT provide you with an intuitive notion of what is going on. This is the most difficult part to learn. For example when studying group theory for physics (QM and field theory) you will need to have a notion of what this mathematical formalism is trying to achieve in "physical terms". I mean, for example it is very important to understand how group theory works in physics.
"Basically you want an equation to be invariant under some transformations. In order to achieve that, the elementary building blocks of this system need to transform according to the socalled irreducible representations of the symmetry group at hand. Quantumnumbers are used to denote these irreducible representations". "For example, if you want the probability of a wavefunction to be invariant under rotations, the wavefunction itself will have to transform as an irreducible representation of the rotation group"
If you are able to translate this in mathematical terms and apply this onto some field equation, you will very soon realize that the use of group theory in field theory is always analoguous. Then you will also be able to comprehend why a phonon has spin 0, why there are only 8 gluons and why a baryon exists out of 3 quarks and a meson out of 2 quarks. Or how quantumnumbers are "born" and why you have only that many values for the magnetic quantum number
I suppose, what i want to say here is : GO TO COLLEGE and BUY THOSE BOOKS, AND START STUDYING. You should not ask such questions like "what do i need to study for ..." here in a public forum. Go consult your student advisor at college.
marlon