There is a joke I have read among mathematicians that to a physicist a group is a lie group without the manifold structure. This more and more as time goes on is becoming an unfair statement but I can easily imagine a time when that clearly captured the times. After all as physicists we are more likey to come across the rotation group before we know what a dihedral group is. Of course from a physics point of view, not knowing more about group theory is clearly becoming anachronisitic and somewhat of an intellectual luddite. One needs to merely open up a book on condensed matter physics and see just how important discrete groups and their representations are in understanding physical systems. These notes are meant for someone who does not want to relegate their knowledge of group theory to the 2 pages of introduction given a physics textbook and on the other hand does not dare open up a math textbook. These notes are meant to be a bridge, but it should be clearly stated that the best way to understand mathematics is to learn who mathematicians think of it.