The Third Man is a noir thriller set in postwar Vienna which tells the story of a couple of Americans trying to renew a childhood friendship in a foreign country after growing up to be very different people. Like all of Graham Greene's fiction, the film makes themes of betrayal, the loss of innocence, and the true difficulty of forming apparently simple moral judgements.
Many people count this as their favourite movie, which is remarkable for a British film of the 1940s. It is just a very successful coming-together of many wonderful talents: Greene wrote a classic screenplay, Carol Reed's direction is inspired genius, and Orson Welles, Trevor Howard, Joseph Cotton and others contributed unforgettable performances. Anton Karas's theme music is legendary. The cinematography is stunning.
You can become obsessed with this film, and if you do you will want to read Charles Drazin's excellent 1999 book "In Search of the Third Man". I also recommend the reviews by the eminent British critic Philip French, who has much of interest to say about the sources for Greene's screenplay.