The Ultima series is split into three books and each book has three chapters, making nine games in the main series total.  There were some side games, but I have not played them as much, and care more for the main series than the side games.

The first book was called the "Age of Darkness", it told of a story of a wizard, his wife, and their demon child offspring.  The first chapter and game follows the hero from another world on his quest to save the world from the evil wizard Mondain.  The second game follows the same hero yet again on a quest to defeat his wife Minax.  The third game follows the same hero once again as he defeats their brain child Exodus.

The second book was called the "Age of Enlightenment", it told of the hero from the other world going through Avatarhood and becoming the Avatar.  After the forth game, "Quest of the Avatar", the hero from the other world is now referred to as the "Avatar" and is called upon for any trouble the people may face.  This is also the first game which the world is now referred to as "Britannia".  The second chapter in the second book, also called Ultima V, the "Avatar" is called upon to save their world from the Shadowlords and ultimately save Lord British from the underworld who was an expedition to explore the newly created caverns.  The codex was recovered in this game and little did the Avatar know what this will cause in his next adventure.  The final chapter in the second book, also called Ultima VI, the Avatar finds out about a new enemy, the Gargoyles who consider him to the "False Prophet".  I will not go further into the plot as this game is very good and a must play in the series.

The third book was called the "Age of the Guardian", it told of a destroyer of worlds calling himself "The Guardian".  This evil is attempting to enter Britannia and conquer it, as he did to previous worlds.  Ultima VII had two parts which follow directly after one another.  In Ultima VIII the Avatar is placed in one of the worlds which the Guardian had taken over.  The final Ultima IX, which definitely received mixed fan reviews due to the story not correctly following the previous games in the series or rather in the third book.  To most fans it was a total disappointment, this was due to the EA Games take over which happened during it's development.