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From The PSUPedia
This is a list of all the story missions that appear in PSP. They are only accessible in story mode and each can only be played through once in a single playthrough (although they can be cancelled before completion and restarted). Each chapter is split into several acts, which are played one after the other. If you abandon a story mission and restart you will begin at the start of the act you were on upon abandoning the mission.
For free and download missions please see the following articles: