Subject: Group Theory and Physics

I have heard that group theory forms and interesting part of the study 
of quantum field theory.  I have studied group theory proper, but i 
would like to know what role group theory plays in physics. does this 
just come from the "reduction" of a vector space to a group? what are 
some examples of groups considered in physics? what are some 
current group flavored problems? does the theory have a rigorous 
foundation? ...?  Where do physicists learn about group theory :) ?   

Re: Group Theory and Physics