The Duke meets with Friar Peter just outside the city and gives him.... a bunch of letters. (What is it with the Duke and letters?)
Duke Vincentio instructs Friar Peter to deliver the letters to him (the Duke) when the time is right.
We learn that the Provost knows of the Duke's elaborate scheme to "return" to Vienna and fix the big mess Angelo has made. (We don't know the details of the plot at this point, but we can guess that the Duke is planning a big "Aha!" moment where he reveals Angelo's crime.)
A guy named Varrius shows up and takes a walk with the Duke. (We're guessing the Duke lets him in on his secret plans.)