The battle for the Falklands by Max Hastings and Simon Jenkins.

Probably the definitive story of the Falklands war, written by one of the few war correspondents that accompanied the Task Force, and an experienced Whitehall journalist. Between them the run-up to the war and its execution is described fully. As usual in a Hastings book judgment is clear and ubiquitous, and shows not only the difference in quality between the opposing forces but also the strengths and weaknesses inside each force.

A very clear and understandable story of the war, and I recommend it as an introduction to the study of its history.