I am familiar with the representation theory of finite groups and Lie groups/algebra from the mathematical perspective, and I am wondering how quantum mechanics/quantum field theory uses concepts from representation theory. I have seen the theory of angular momentum in quantum mechanics, and I realized that Lx, Ly, and Lz, the components of angular momentum, are elements of the Lie algebra SO(3). I also heard of the notion that irreducible representations correspond with elementary particles and that the Casimir element can measure scalar quantities such as mass. Unfortunately, my knowledge in this area is merely a bunch of scattered facts. Could anyone explain the foundations of the relationship between representation theory and quantum physics, or provide a resource (book or website) that explains this connection? Thanks.