I can recommend Howards Georgi's Lie Algebras in Particle Physics which is a good introduction in the context of particle physics (yes, it covers both Lie algeb

I can recommend Howards Georgi's Lie Algebras in Particle Physics which is a good introduction in the context of particle physics (yes, it covers both Lie algebras and groups). No, it is nothing like the angular momentum of a spinning object. The name is rooted in a historical misconception. It is a form on angular momentum, which caused the misunderstanding. As of today, we still do not have a deeper understanding of spin in quantum mechanics: it's just some intrinsic angular momentum with SU(2) symmetry, and the value of angular momentum is in general different between particles (corresponding to the irreducible representations of SU(2), and the angular momentum is mostly 1/2 or 1 in units of reduced Planck constant except for some exotic/composite particles).