Battle For The Falklands by Max Hastings & Simon Jenkins gives a good background to the political mess that resulted in Op Corporate, and a reasonable coverage of the military side. For more specific reading there is a list at http://www.naval-history.net/F01Books.htm
I enjoyed 'Reasons in Writing' by Ewen Southby-Tailyour. A Royal Marine who, despite his father being CG of the RM had been somewhat side-lined due to a clash with his then CO and sent down as OC of Naval Party 8901 (standing by to be corrected on the number) in the Falklands in the last days of the 70s. He upset 'the system' by taking his wife and 2 small children on the unaccompanied posting, but he also shipped down his yacht on which he then spent a year mapping the beaches around the islands in his spare time. On comes the Falklands War and all of a sudden, the sidelined Marine is suddenly the best-qualified advisor that the Task Force Commander could need!
For an overall view, try The Official History of the Falklands Campaign (Vols I & II) as revised and updated in 2007 by Lawrence Freedman, Professor of War Studies at King's College London where he is currently Vice Principal. The action accounts are in Vol II (War and Diplomacy).