TITLE: Schur-Weyl Duality ( Classical ) and the Double Commutant reference request
QUESTION [16 upvotes]: I would like to ask for any reference suggestions on the topic of Schur-Weyl Duality for GLn ( directly GLn, not through the lie algebra ) and the double commutant theorem. 
The section on this material from Fulton and Harris' "Representation Theory" book should suit my needs, but I find the proofs in the book a little hard to read ( for example, in the middle of the proof, use some sort of "isomorphism of ideals", although an isomorphism of ideals is not mentioned anywhere ). So, the organization, definitions and skeleton from the Fulton-Harris book is good for me, but I cannot really understand the proofs.
A book, notes/lecture notes, or anything online..etc would be nice. 
Thank you

REPLY [8 votes]: Despite of very detailed and excellent answer from BenjaLim, let me also list some reference I used (my background is more symmetric group representation theoretic, rather than Lie theoretic, so this gives an alternate flavour to what BenjaLim suggested)
(1) Goodman-Wallach "Representations and Invariants of Classical Groups"; which I think is the clearest reference I have ever read (advantage: they setup double commutant theory abstractly and develop SW duality from that)
(2) Martin "Schur algebras and representation theory"; there are some steps which he skipped, but can be done as an exercise.  The term "Schur-Weyl duality" is never used in the text, and the actual "Proof" is scattered in different parts of the book, though not very hard to spot.
(3) Etingof's course notes "Introduction to Representation Theory", this looks more like a concise version of Goodman-Wallach.
In a way, I should list Green's book "Polynomial Representation of GL_n", which is what my advisor recommended me to read, but if you just want "Schur-Weyl duality" without the appearance of Schur algebra, then this is not recommended, as it will take quite a long way to get to SW duality.
Also see this Math.SE question: Understanding the proof of Schur-Weyl Duality