I am having an issue with my studying: I am focusing on C*-algebra theory, but I am encountering many propositions that have to do with von Neumann algebras. I cannot understand the ultraweak topology, especially the fact that it is independent of the representation $M\subset B(H)$. I cannot understand what that means, since by the definition I have encountered von Neumann algebras are defined to live in some $B(H)$. I also cannot understand what we mean when we say normal representation/ functional. I would like to understand these terms but I do not know where to study from. Other notions I am encountering are the enveloping von Neumann algebra and the double dual of a $C^*$-algebra and the isometric isomorphism between the two.
I am looking for a reference to study these concepts but as I said, this is not my focus so I do not want to deal with all the details. A short presentation would be fine for me. Right now I have seen the definition of a von Neumann algebra as a $*$-subalgebra of some $B(H)$ that is closed in SOT, the equivalence of it being closed in WOT, the double commutant theorem, the fact that vN algebra's are always unital, the fact that they are closed under polar decomposition and that they contain many projections (i.e. they are the norm-closed linear span of their projections). I have also seen Kaplansky's density theorem. Oh, I have also seen the construction of a predual through the trace-class operators and all, but it never came in handy.
Any suggestions? I tried Kadison and Ringrose but their presentation seems way too detailed for me.