When Alonso and Prospero meet at the end of the play, as each other (since Prospero dressed up as a magician at first) they forgive each other, finally. Alonso has already renounced what he did to Prospero and restores his Dukedom. When they do meet, Prospero says, "Let us not burden our remembrances with / A heaviness that's gone" (V.i.199-200), urging Alonso to forget the past.
alonso is really sorry for taking his dukedom and he gives it back. he is really happy to have his son back and he gives his permission for ferdinand and miranda to marry.