This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
Once you have the Odin Esper, you can convert him to the Raiden Esper.
Have a scholarly conversation with one of Figaro's scholars. He will
give you an important clue on how you can do so. Head back to the Throne
Room of the Ancient Castle and try it.
Give up? Read on...
Go to the Throne Room of the Ancient Castle. Step into the Queen's
Throne (the rightmost throne), step forward five times from the seat of
the throne, and press A. Head back to the Queen's Room, and head down
the stairs. Find the Queen's Statue, and the Esper will be converted.
Careful! Odin is the _only_ Esper in the game which can increase your
characters' speed. Without Odin, you will never be able to increase your
characters' speed, and once you have Raiden, there's no turning back.