For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
Barabas, formerly Head Merchant in Control of Malta, is stripped of all of his wealth and property by Ferneze to pay off the threatening Turkish Empire. Barabas, totally ticked off, starts planning the deaths of Mathias and Lodowick, Ferneze's son. Plus, he wants his money back.
Act II
Barabas kills lot of people. No, really, that's mostly what's going on for middle part of the play. He's eventually found out and left for dead outside the walls of Malta. Barabas then helps the Turks invade Malta, who in return make him Governor.
Act III
Barabas's plot number … something involves destroying the Turkish army. Instead, Ferneze betrays him and he ends up dying in the trap he had devised for Calymath, the Turkish leader. Ferneze regains control of Malta and ransoms Calymath for the restoration of Malta.